Quelle  ctosylno.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctosylno.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of the Sylow normalizers
##  of sporadic simple groups.
##  Many of these tables have been published in~\cite{Ost86},
##  they are marked by `"origin: Ostermann"' in their `InfoText' value.
##
#T  change: The primes are listed up in brackets after the group names.
##
##  $M_{11}$, $M_{12}$, $M_{22}$, $M_{23}$, $M_{24}$ (2,3 for each),
##
##  $J_1$ (2), $J_2$ (2,3,5), $J_3$ (2,3), $J_4$ (3,11),
##
##  $HS$, $McL$, $Suz$, $Ru$ and $Ly$ (2,3,5 for each),
##
##  $ON$ (2,3,7), $He$ (2,3,5,7), $Co_1$ (3,7), $Co_2$ (5),
##  $Co_3$ (2,3,5), $Fi_{22}$ (3,5) and $Th$ (2).
##
##  *Note* the isomorphisms $M22N2 \cong M23N2$, $M24N2 \cong HeN2$,
##  $M24N3 \cong HeN3$, and $Co2N5 \cong ThN5$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctosylno.tbl,v $
#H  Revision 4.56  2012/06/20 14:45:32  gap
#H  added tables and fusions, as documented in ctbldiff.dat
#H      TB
#H
#H  Revision 4.55  2012/06/06 12:44:28  gap
#H  added the table of "ThN3"
#H      TB
#H
#H  Revision 4.54  2012/04/23 16:16:16  gap
#H  next step of consolidation:
#H
#H  - removed a few unnecessary duplicate tables,
#H    and changed some related fusions, names of maxes, table constructions
#H  - make sure that duplicate tables arise only via `ConstructPermuted'
#H    constructions
#H  - added some relative names
#H  - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H    L2(41) -> M, (A5xA12):2 -> A17,
#H  - added maxes of A12.2, L6(2), 2.M22.2
#H  - added table of QD16.2,
#H  - fixed the syntax of two `ALN' calls
#H      TB
#H
#H  Revision 4.53  2012/03/28 13:11:43  gap
#H  added missing fusion Fi22N5 -> 2F4(2)'.2
#H      TB
#H
#H  Revision 4.52  2011/09/28 14:08:59  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added tables of Fi22N2, S4x5^2:4S4,
#H  - added fusions 3^(1+2):8","U3(3), 3^(1+2):D8","3.A6.2_1,
#H    3^(1+2):D8 -> 3.A7.2, 3^(1+2):D8 -> 2^6:3^(1+2).D8,
#H    3^(1+2):SD16 -> 2F4(2)'.2, 3^4:(3^2:Q8) -> McL.2N3,
#H    3^4:2^(1+4)D10 -> 3^4:2^(1+4).(5:4), 4^3.D8 -> ON.2N2,
#H    5^(1+2):3:8 -> 5^(1+2):(24:2), 7^(1+2):(D8x3) -> 7^(1+2)_+:(3xD16),
#H    7^(1+2):(S3x6) -> 7^(1+2)_+:(6xS3).2, Co1N3 -> Co1,
#H    Fi22N5 -> O8+(2).3.2, McLN2 -> McL.2N2, 2.HSN3 -> 2.HS.2N3,
#H    Co1N5 -> 5^(1+2):GL2(5), F3+N5 -> S4x5^2:4S4,
#H      TB
#H
#H  Revision 4.51  2011/02/09 15:56:57  gap
#H  name 11^2:(5x2A5) (used in AtlasRep) for 11^2:(5x2.A5)
#H      TB
#H
#H  Revision 4.50  2010/12/01 17:47:57  gap
#H  renamed "Sym(4)" to "Symm(4)";
#H  note that the table constructed with `CharacterTable( "Symmetric", 4 )'
#H  gets the identifier `"Sym(4)"', and this table is sorted differently
#H      TB
#H
#H  Revision 4.49  2010/05/05 13:20:08  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.48  2010/01/19 17:05:35  gap
#H  added several tables of maximal subgroups of central extensions of
#H  simple groups (many of them were contributed by S. Dany)
#H      TB
#H
#H  Revision 4.47  2009/07/29 14:00:54  gap
#H  added fusions 13:12 -> 2F4(2)'.2, 13:12 -> A13.2
#H      TB
#H
#H  Revision 4.46  2009/05/11 15:28:36  gap
#H  added table of MN7
#H      TB
#H
#H  Revision 4.45  2009/04/22 12:39:07  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.44  2009/03/31 16:33:40  gap
#H  added fusion 3^2:Q8 -> L3(4)
#H      TB
#H
#H  Revision 4.43  2009/01/07 09:37:38  gap
#H  added table of HNN2,
#H  added fusion 3^4:2^(1+4).(5:4) -> ON.2
#H      TB
#H
#H  Revision 4.42  2008/06/24 16:12:49  gap
#H  "2.HS.2N5" is "2.HS.2M9" not "2.HS.2M3"
#H  added table of ON.2M5
#H      TB
#H
#H  Revision 4.41  2007/07/03 08:51:54  gap
#H  added fusions,
#H  encoded several tables as index two subdirect products
#H      TB
#H
#H  Revision 4.40  2007/06/05 07:52:55  gap
#H  unified the tables of "3^2:Q8.2" and "3^2:SD16"
#H      TB
#H
#H  Revision 4.39  2006/06/07 07:29:37  gap
#H  added comment to the fusion BN7 -> B
#H      TB
#H
#H  Revision 4.38  2004/08/31 12:33:33  gap
#H  added tables of 4.L2(25).2_3,
#H                  L2(49).2^2,
#H                  L2(81).2^2,
#H                  L2(81).(2x4),
#H                  3.L3(4).3.2_2,
#H                  L3(9).2^2,
#H                  L4(4).2^2,
#H                  2x2^3:L3(2)x2,
#H                  (2xA6).2^2,
#H                  2xL2(11).2,
#H                  S3xTh,
#H                  41:40,
#H                  7^(1+4):(3x2.S7),
#H                  7xL2(8),
#H                  (7xL2(8)).3,
#H                  O7(3)N3A,
#H                  O8+(3).2_1',
#H                  O8+(3).2_1'',
#H                  O8+(3).2_2',
#H                  O8+(3).(2^2)_{122},
#H                  S4(9),
#H                  S4(9).2_i,
#H                  2.U4(3).2_2',
#H                  2.U4(3).(2^2)_{133},
#H                  2.U4(3).D8,
#H                  3.U6(2).S3,
#H  added fusions 3.A6.2_i -> 3.A6.2^2,
#H                L2(49).2_i -> L2(49).2^2,
#H                L3(9).2_i -> L3(9).2^2,
#H                L4(4).2_i -> L4(4).2^2,
#H                G2(3) -> O7(3),
#H                L2(17) -> S8(2),
#H                2.L3(4).2_2 -> 2.M22.2
#H                3.L3(4).2_2 -> 3.L3(4).3.2_2
#H                3.L3(4).3 -> 3.L3(4).3.2_2
#H                2^5:S6 -> 2.M22.2
#H                O8+(3) -> O8+(3).2_1',
#H                O8+(3) -> O8+(3).2_1'',
#H                O8+(3) -> O8+(3).2_2',
#H                O8+(3) -> O8+(3).(2^2)_{122},
#H                O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H                O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H                2.U4(3) -> 2.U4(3).2_2',
#H                2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_2 -> O7(3),
#H                2.U4(3).2_2' -> U4(3).2_2,
#H                2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).4 -> 2.U4(3).D8,
#H                3.U6(2).2 -> 3.U6(2).S3,
#H                3.U6(2).3 -> 3.U6(2).S3,
#H  replaced table of psl(3,4):d12 by L3(4).D12,
#H  changed table of O8+(3).S4 to a construction table,
#H  changed encoding of the table of 12.A6.2_3,
#H  added maxes of Sz(8), Sz(8).3,
#H      TB
#H
#H  Revision 4.37  2004/01/20 10:26:13  gap
#H  added several names of the forms `<name>C<class>', `<name>N<class>'
#H      TB
#H
#H  Revision 4.36  2004/01/09 08:36:42  gap
#H  replaced fusion F3+N5 -> F3+ by a smaller one (had not been available
#H  in GAP 4.3)
#H      TB
#H
#H  Revision 4.35  2003/11/17 15:49:55  gap
#H  added a few obvious fusions
#H      TB
#H
#H  Revision 4.34  2003/11/14 08:38:47  gap
#H  fixed an InfoText
#H      TB
#H
#H  Revision 4.33  2003/11/12 17:38:37  gap
#H  removed name "HS.2M2" for "HS.2N5"
#H  corrected name F3+17 to F3+N17 (for 17:16)
#H      TB
#H
#H  Revision 4.32  2003/05/15 17:38:24  gap
#H  next step towards the closer connection to the library of tables of marks:
#H  added fusions tbl -> tom, adjusted fusions between character tables
#H  in order to make the diagrams commute, adjusted orderings of maxes
#H      TB
#H
#H  Revision 4.31  2003/03/07 15:53:41  gap
#H  added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H  and many `tomidentifier' components (still several are missing)
#H      TB
#H
#H  Revision 4.30  2003/01/24 15:57:39  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.29  2003/01/21 16:25:32  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.28  2003/01/14 17:28:50  gap
#H  changed `InfoText' values (for a better programmatic access)
#H  and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H  there is only one factor (again better programmatic handling)
#H      TB
#H
#H  Revision 4.27  2003/01/13 17:18:37  gap
#H  added fusion 2.HS.2N5 -> 5^(1+4):2^(1+4).5.4
#H      TB
#H
#H  Revision 4.26  2003/01/03 10:10:22  gap
#H  added fusions M24N2 -> M24 and -> He
#H      TB
#H
#H  Revision 4.25  2002/11/04 16:33:47  gap
#H  added fusions of maxes of U3(3).2,
#H  added fusion U3(3).2 -> Fi24' (this took me a whole afternoon ...)
#H      TB
#H
#H  Revision 4.24  2002/10/14 15:19:43  gap
#H  added a fusion text
#H      TB
#H
#H  Revision 4.23  2002/09/23 15:06:00  gap
#H  added fusions SuzN3 -> Suz, Co3N5 -> Co3,
#H  and names "McL.2N5", "U3(5).3.2N5"
#H      TB
#H
#H  Revision 4.22  2002/09/18 15:22:01  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.21  2002/09/05 15:12:16  gap
#H  fixed fusion comments (will be used programmatically in the future),
#H  corrected fusion (2^2xD14):3 -> Ru,
#H  removed name `rvn2' for `RuN2',
#H  removed names `mcn2', `mcn3', `mcn5',
#H  added fusions 2^4:D8 -> M23,
#H                3^(1+2):8 -> J2,
#H                3^(1+2):D8 -> M24,
#H                3^(1+2):D8 -> He,
#H                3^(1+2):SD16 -> Ru,
#H                3^2:SD16 -> M23,
#H                3^4:(3^2:Q8) -> McL,
#H                4^3.D8 -> ON,
#H                5^2:(4xS3) -> Suz,
#H                7^(1+2):(D8x3) -> ON,
#H                Co3N2 -> Co3,
#H                Co3N3 -> Co3,
#H                J2N2 -> J2,
#H                J3N2 -> J3,
#H      TB
#H
#H  Revision 4.20  2002/08/21 13:53:51  gap
#H  removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H      TB
#H
#H  Revision 4.19  2002/08/01 13:20:55  gap
#H  removed names c3n5, c1n3, c3n2, c3n3
#H      TB
#H
#H  Revision 4.18  2002/07/26 16:58:05  gap
#H  added more missing table automorphisms,
#H  removed a few inconvenient names such as `c2' for `Co2'
#H  (note that `c2' is used for the cyclic group of order 2,
#H  which occurs in direct product constructions ...)
#H      TB
#H
#H  Revision 4.17  2002/07/24 16:41:46  gap
#H  added power maps and fusion for Fi22N3,
#H  added table of MN11
#H      TB
#H
#H  Revision 4.16  2002/07/18 17:19:04  gap
#H  ... and adjusted the table automorphisms!
#H      TB
#H
#H  Revision 4.15  2002/07/18 17:14:36  gap
#H  added power map and fusion for ThN2
#H      TB
#H
#H  Revision 4.14  2002/07/17 15:19:30  gap
#H  added missing power maps and fusion to SuzN2,
#H  added tables of RuN7, RuN13
#H      TB
#H
#H  Revision 4.13  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.12  2002/07/08 16:06:57  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.11  2002/05/16 15:08:14  gap
#H  replaced the new 2nd power map of RuN2 by an equivalent one
#H  that is compatible with the stored fusion
#H      TB
#H
#H  Revision 4.10  2002/04/18 16:32:59  gap
#H  added fusion M22N3 -> M22, nd 2nd power map of RuN2
#H      TB
#H
#H  Revision 4.9  2002/03/25 18:17:00  gap
#H  added J4N3 (the correct table!), F3+N7, M24N5, Co2N2, Co2N3, Co2N7, MN13
#H      TB
#H
#H  Revision 4.8  2002/03/04 17:14:34  gap
#H  added tables of 2x5:4, 11:5, 2x11:5, 17:8, 17:16, 19:9, M23N5,
#H  7:3xS3, S3x7:6, Co1N5, F3+N5, BN7
#H      TB
#H
#H  Revision 4.7  2001/05/04 16:50:08  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.7 of ctbllib coincides with Rev. 4.6 of tbl in GAP 4)
#H
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctosylno.tbl,v
#H  Working file: ctosylno.tbl
#H  head: 4.6
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.6.0.6
#H   GAP4R2PRE2: 4.6.0.4
#H   GAP4R2PRE1: 4.6.0.2
#H   GAP4R1: 4.4.0.2
#H  keyword substitution: kv
#H  total revisions: 8; selected revisions: 8
#H  description:
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/10/22 13:24:48;  author: gap;  state: Exp;  lines: +10 -3
#H  added maxes of J2.2
#H
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/10/21 14:15:48;  author: gap;  state: Exp;  lines: +15 -3
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H
#H  added maxes of McL.2,
#H
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1999/07/14 11:39:42;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1999/03/25 12:33:26;  author: gap;  state: Exp;  lines: +3 -3
#H  added fusions into S10(2)
#H
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 15:45:50;  author: gap;  state: Exp;  lines: +15 -7
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:47:20;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.2
#H  date: 1996/12/17 12:49:22;  author: sam;  state: Exp;  lines: +55 -2
#H  added some fusions into '2.HS', and table of '2.HSN3'
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:01:44;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("(3^(1+2)x2).SD16",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Note that this is NOT the table of the Sylow 3 normalizer J4,\n",
"contrary to the claim in Ostermann's book"
],
[864,864,864,864,24,24,432,72,72,48,48,24,24,432,432,432,72,72,72,72,72,72,24,
24,24,24,48,48,48,48,48,48,48,48,24,24,24,24,48,48,48,48,48,48,48,48],
[,[1,1,1,1,1,1,7,8,9,2,2,2,2,7,7,7,8,8,9,9,8,9,8,8,8,8,10,10,10,10,15,15,15,
15,20,20,20,20,32,32,31,31,32,32,31,31],[1,2,3,4,5,6,1,1,1,10,11,12,13,3,2,4,
3,2,3,2,4,4,5,5,6,6,27,28,29,30,10,10,11,11,12,12,13,13,27,28,28,27,29,30,30,
29]],
[[1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,
1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1],[1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[1,
1,-1,-1,1,-1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1,
-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,-2,2,0,0,2,2,2,0,0,0,0,-2,-2,2,-2,-2,-2,-2,2,2,0,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,0,E(8)+E(8)^3,
-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3],
[TENSOR,[9,5]],
[TENSOR,[9,2]],
[TENSOR,[9,1]],[2,2,-2,-2,0,0,2,2,2,-2,2,0,0,-2,2,-2,-2,2,-2,2,-2,-2,0,0,0,0,
0,0,0,0,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,1]],[4,-4,-4,4,0,0,4,-2,1,0,0,0,0,-4,-4,4,2,2,-1,-1,-2,1,0,0,0,0,
0,0,0,0,0,0,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0,0,0,0,0,0,0],
[TENSOR,[15,4]],
[TENSOR,[15,1]],
[TENSOR,[15,3]],[4,4,-4,-4,0,0,4,-2,1,0,0,-2,2,-4,4,-4,2,-2,-1,1,2,-1,0,0,0,0,
0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[19,1]],
[TENSOR,[19,4]],
[TENSOR,[19,3]],[4,-4,-4,4,0,0,4,1,-2,0,0,0,0,-4,-4,4,-1,-1,2,2,1,-2,
E(3)-E(3)^2,-E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[23,3]],
[TENSOR,[23,2]],
[TENSOR,[23,1]],[4,4,-4,-4,-2,2,4,1,-2,0,0,0,0,-4,4,-4,-1,1,2,-2,-1,2,1,1,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,3]],
[TENSOR,[27,2]],
[TENSOR,[27,1]],[6,-6,6,-6,0,0,-3,0,0,0,0,0,0,-3,3,3,0,0,0,0,0,0,0,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0,0,E(24)+E(24)^11,
-E(24)-E(24)^11,-E(24)^17-E(24)^19,E(24)^17+E(24)^19,E(24)+E(24)^11,
-E(24)-E(24)^11,-E(24)^17-E(24)^19,E(24)^17+E(24)^19],
[TENSOR,[31,5]],
[GALOIS,[31,17]],
[TENSOR,[33,5]],
[TENSOR,[31,2]],
[TENSOR,[31,1]],
[TENSOR,[33,2]],
[TENSOR,[33,1]],[6,6,6,6,0,0,-3,0,0,-2,-2,0,0,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,-2,
-2,-2,-2,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1],
[TENSOR,[39,5]],
[TENSOR,[39,2]],
[TENSOR,[39,1]],[6,6,6,6,0,0,-3,0,0,2,2,0,0,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-1,-1,-1,-1,0,0,0,0,E(12)^7-E(12)^11,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11],
[TENSOR,[43,5]],
[TENSOR,[43,2]],
[TENSOR,[43,1]]],
[(35,36)(37,38),(31,32)(33,34)(35,36)(37,38)(39,42)(40,41)(43,46)(44,45),
(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,41)(40,42)(43,45)(44,46),(23,24)
(25,26),(23,24)(25,26)(31,32)(33,34)(35,36)(37,38)(39,42)(40,41)(43,46)
(44,45),( 5, 6)(12,13)(23,25)(24,26)(35,37)(36,38),(31,32)(33,34)(39,42)
(40,41)(43,46)(44,45),(27,28)(29,30)(39,40)(41,42)(43,44)(45,46),(12,13)
(27,29)(28,30)(35,37)(36,38)(39,43)(40,44)(41,45)(42,46),( 3, 4)(14,16)(17,21)
(19,22)(25,26)(29,30)(33,34)(37,38)(43,44)(45,46)]);
ARC("(3^(1+2)x2).SD16","CAS",[rec(name:="j4n3",
permchars:=(),
permclasses:=(),
text:="")]);

MOT("(2x3^(1+2)_+:8):2",
[
"origin: Dixon's Algorithm,\n",
"Sylow 3 normalizer in the sporadic simple Janko group J4\n",
"(Note that the table printed in Ostermann's book is not related to J4.),\n",
"maximal subgroup of 6.L3(4).2_2"
],
[864,864,432,432,36,36,96,96,48,48,48,48,24,24,16,16,16,16,24,24,24,24,12,12,
24,24,24,24],
[,[1,1,3,3,5,5,1,1,3,3,7,7,9,9,12,12,12,12,1,1,8,8,5,5,10,10,10,10],[1,2,1,2,1
,2,7,8,7,8,11,12,11,12,18,17,16,15,19,20,22,21,19,20,22,22,21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[6,3]],[8,8,8,8,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,1,1,0,0,0,0],
[TENSOR,[8,2]],[6,6,-3,-3,0,0,-2,-2,1,1,2,2,-1,-1,0,0,0,0,0,0,2,2,0,0,-1,-1,
-1,-1],
[TENSOR,[10,2]],[6,6,-3,-3,0,0,-2,-2,1,1,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,
-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2],
[TENSOR,[12,2]],[12,12,-6,-6,0,0,4,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,E(4),E(4),-E(4),-E(4),1,-1,E(4),-E(4),1
,-1,E(4),E(4),-E(4),-E(4)],
[TENSOR,[15,4]],
[TENSOR,[2,16]],
[TENSOR,[2,15]],
[TENSOR,[5,15]],
[TENSOR,[6,16]],
[TENSOR,[6,15]],
[TENSOR,[12,16]],
[TENSOR,[12,15]],
[TENSOR,[10,16]],
[TENSOR,[10,15]],
[TENSOR,[8,15]],
[TENSOR,[8,17]],
[TENSOR,[14,15]]],
[(15,16)(17,18),(25,26)(27,28),(15,17)(16,18)(19,20)(23,24),
(15,17)(16,18)(21,22)(25,27)(26,28)]);
ALF("(2x3^(1+2)_+:8):2","J4",[1,2,4,9,4,10,2,3,10,11,6,5,22,21,14,14,14,
14,2,3,7,7,10,11,23,23,23,23],[
"determined by factorization through 6.L3(4).2_2 and 6.M22.2"
]);
ALF("(2x3^(1+2)_+:8):2","2.Ru",[1,2,6,7,6,7,3,4,18,19,8,9,30,31,22,22,23,
23,3,4,10,11,18,19,32,32,33,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("(2x3^(1+2)_+:8):2","6.L3(4).2_2",[1,4,3,2,9,10,5,8,7,6,11,14,13,12,
38,38,39,39,32,33,15,15,36,37,16,17,16,17],[
"fusion map is unique up to table automorphisms"
]);
ALF("(2x3^(1+2)_+:8):2","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,2,2,4,4,1,3,2,4,
1,3,2,2,4,4]);
ALF("(2x3^(1+2)_+:8):2","3^(1+2):SD16",[1,1,4,4,5,5,2,2,8,8,6,6,14,14,10,
11,11,10,3,3,7,7,9,9,12,13,12,13]);
ALN("(2x3^(1+2)_+:8):2",["J4N3","6.L3(4).2_2M6","6.L3(4).2_2N3","2.RuN3"]);

MOT("11+^(1+2):(5x2S4)",
[
"origin: Ostermann\n",
"tests: 1.o.r., pow[2,3,5,11]\n",
"Maximal subgroup in sporadic Janko group J4."
],
[319440,2640,220,330,440,240,240,240,240,330,40,40,240,240,240,240,20,20,20,
20,30,30,30,30,40,40,40,40,30,30,30,30,40,40,40,40,40,40,40,40,31944,242,264,
22,66,66,44,66,66],
[,[1,1,1,4,2,7,9,6,8,4,5,5,7,6,9,8,7,6,9,8,22,23,24,21,13,14,15,16,21,22,24,
23,25,26,27,28,26,27,25,28,41,42,41,42,45,46,43,45,46],[1,2,3,1,5,8,6,9,7,2,
11,12,14,16,13,15,18,20,17,19,6,7,9,8,26,28,25,27,14,13,16,15,34,36,39,38,40,
33,37,35,41,42,43,44,41,41,47,43,43],,[1,2,3,4,5,1,1,1,1,10,12,11,2,2,2,2,3,3,
3,3,4,4,4,4,5,5,5,5,10,10,10,10,11,11,12,11,12,11,12,12,41,42,43,44,46,45,47,
49,48],,[1,2,3,4,5,7,9,6,8,10,12,11,15,13,16,14,19,17,20,18,22,23,24,21,27,25,
28,26,30,32,29,31,35,39,36,37,33,40,38,34,41,42,43,44,46,45,47,49,48],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,1,1,2,3,4,4,5,10,10],,[1,2,3,4,5,8,6,9,7,10,12,
11,14,16,13,15,18,20,17,19,24,21,22,23,26,28,25,27,31,29,32,30,37,40,33,35,36,
39,34,38,41,42,43,44,46,45,47,49,48],,,,[1,2,3,4,5,7,9,6,8,10,11,12,15,13,16,
14,19,17,20,18,22,23,24,21,27,25,28,26,30,32,29,31,38,33,40,34,39,36,35,37,41,
42,43,44,45,46,47,48,49],,[1,2,3,4,5,9,8,7,6,10,11,12,16,15,14,13,20,19,18,17,
23,24,21,22,28,27,26,25,32,31,30,29,36,38,37,33,35,34,40,39,41,42,43,44,46,45,
47,49,48],,,,[1,2,3,4,5,8,6,9,7,10,12,11,14,16,13,15,18,20,17,19,24,21,22,23,
26,28,25,27,31,29,32,30,37,40,33,35,36,39,34,38,41,42,43,44,46,45,47,49,
48],,,,,,[1,2,3,4,5,9,8,7,6,10,12,11,16,15,14,13,20,19,18,17,23,24,21,22,28,
27,26,25,32,31,30,29,40,35,34,39,38,37,36,33,41,42,43,44,45,46,47,48,49],,[1,
2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,39,37,38,40,34,35,33,36,41,42,43,44,45,46,47,48,49],,,,,,[1,2,3,4,5,
7,9,6,8,10,12,11,15,13,16,14,19,17,20,18,22,23,24,21,27,25,28,26,30,32,29,31,
35,39,36,37,33,40,38,34,41,42,43,44,45,46,47,48,49],,,,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49],,[1,2,3,4,5,8,6,9,7,10,11,12,14,16,13,
15,18,20,17,19,24,21,22,23,26,28,25,27,31,29,32,30,34,36,39,38,40,33,37,35,41,
42,43,44,46,45,47,49,48],,,,[1,2,3,4,5,7,9,6,8,10,12,11,15,13,16,14,19,17,20,
18,22,23,24,21,27,25,28,26,30,32,29,31,35,39,36,37,33,40,38,34,41,42,43,44,46,
45,47,49,48],,,,,,[1,2,3,4,5,8,6,9,7,10,12,11,14,16,13,15,18,20,17,19,24,21,
22,23,26,28,25,27,31,29,32,30,37,40,33,35,36,39,34,38,41,42,43,44,46,45,47,49,
48],,,,,,[1,2,3,4,5,9,8,7,6,10,11,12,16,15,14,13,20,19,18,17,23,24,21,22,28,
27,26,25,32,31,30,29,36,38,37,33,35,34,40,39,41,42,43,44,46,45,47,49,48],,[1,
2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,39,37,38,40,34,35,33,36,41,42,43,44,46,45,47,49,48]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,E(5)^4,E(5)^3,E(5)^2,E(5),1,-1,-1,E(5)^4,
E(5)^2,E(5)^3,E(5),-E(5)^4,-E(5)^2,-E(5)^3,-E(5),E(5)^3,E(5),E(5)^2,E(5)^4,
E(5)^2,E(5),E(5)^4,E(5)^3,E(5)^4,E(5)^3,E(5)^2,E(5),-E(5),-E(5)^3,-E(5)^2,
-E(5)^4,-E(5)^3,-E(5)^2,-E(5),-E(5)^4,1,1,1,-1,1,1,1,1,1],[1,1,1,1,1,E(5)^4,
E(5)^3,E(5)^2,E(5),1,1,1,E(5)^4,E(5)^2,E(5)^3,E(5),E(5)^4,E(5)^2,E(5)^3,E(5),
E(5)^3,E(5),E(5)^2,E(5)^4,E(5)^2,E(5),E(5)^4,E(5)^3,E(5)^4,E(5)^3,E(5)^2,E(5),
E(5),E(5)^3,E(5)^2,E(5)^4,E(5)^3,E(5)^2,E(5),E(5)^4,1,1,1,1,1,1,1,1,1],
[GALOIS,[2,4]],
[GALOIS,[3,4]],
[TENSOR,[4,5]],
[TENSOR,[4,4]],
[TENSOR,[2,3]],
[TENSOR,[2,2]],
[TENSOR,[2,5]],[2,-2,0,-1,0,2*E(5)^4,2*E(5)^3,2*E(5)^2,2*E(5),1,E(8)+E(8)^3,
-E(8)-E(8)^3,-2*E(5)^4,-2*E(5)^2,-2*E(5)^3,-2*E(5),0,0,0,0,-E(5)^3,-E(5),
-E(5)^2,-E(5)^4,0,0,0,0,E(5)^4,E(5)^3,E(5)^2,E(5),-E(40)^13-E(40)^23,
-E(40)^29-E(40)^39,E(40)^21+E(40)^31,-E(40)^7-E(40)^37,E(40)^29+E(40)^39,
-E(40)^21-E(40)^31,E(40)^13+E(40)^23,E(40)^7+E(40)^37,2,2,-2,0,-1,-1,0,1,1],
[TENSOR,[11,10]],[2,2,0,-1,2,2*E(5)^4,2*E(5)^3,2*E(5)^2,2*E(5),-1,0,0,
2*E(5)^4,2*E(5)^2,2*E(5)^3,2*E(5),0,0,0,0,-E(5)^3,-E(5),-E(5)^2,-E(5)^4,
2*E(5)^2,2*E(5),2*E(5)^4,2*E(5)^3,-E(5)^4,-E(5)^3,-E(5)^2,-E(5),0,0,0,0,0,0,0,
0,2,2,2,0,-1,-1,2,-1,-1],
[TENSOR,[11,7]],
[TENSOR,[11,6]],
[TENSOR,[13,6]],
[TENSOR,[11,8]],
[TENSOR,[11,9]],
[TENSOR,[13,8]],
[TENSOR,[11,3]],
[TENSOR,[11,2]],
[TENSOR,[13,2]],
[TENSOR,[11,5]],
[TENSOR,[11,4]],
[TENSOR,[13,4]],[3,3,-1,0,-1,3*E(5)^4,3*E(5)^3,3*E(5)^2,3*E(5),0,1,1,3*E(5)^4,
3*E(5)^2,3*E(5)^3,3*E(5),-E(5)^4,-E(5)^2,-E(5)^3,-E(5),0,0,0,0,-E(5)^2,-E(5),
-E(5)^4,-E(5)^3,0,0,0,0,E(5),E(5)^3,E(5)^2,E(5)^4,E(5)^3,E(5)^2,E(5),E(5)^4,3,
3,3,-1,0,0,-1,0,0],
[TENSOR,[26,10]],
[TENSOR,[26,7]],
[TENSOR,[26,6]],
[TENSOR,[26,9]],
[TENSOR,[26,8]],
[TENSOR,[26,3]],
[TENSOR,[26,2]],
[TENSOR,[26,4]],
[TENSOR,[26,5]],[4,-4,0,1,0,4*E(5)^4,4*E(5)^3,4*E(5)^2,4*E(5),-1,0,0,
-4*E(5)^4,-4*E(5)^2,-4*E(5)^3,-4*E(5),0,0,0,0,E(5)^3,E(5),E(5)^2,E(5)^4,0,0,0,
0,-E(5)^4,-E(5)^3,-E(5)^2,-E(5),0,0,0,0,0,0,0,0,4,4,-4,0,1,1,0,-1,-1],
[TENSOR,[36,6]],
[TENSOR,[36,8]],
[TENSOR,[36,2]],
[TENSOR,[36,4]],[110,-10,0,5,10,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-11,0,1,0,-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16
 -E(33)^17-E(33)^25-E(33)^29-E(33)^31-E(33)^32,-E(33)^5-E(33)^7-E(33)^10
 -E(33)^13-E(33)^14-E(33)^19-E(33)^20-E(33)^23-E(33)^26-E(33)^28,-1,
-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16-E(33)^17-E(33)^25-E(33)^29-E(33)^31
 -E(33)^32,-E(33)^5-E(33)^7-E(33)^10-E(33)^13-E(33)^14-E(33)^19-E(33)^20
 -E(33)^23-E(33)^26-E(33)^28],[110,-10,0,-10,10,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-11,0,1,0,1,1,-1,1,1],
[GALOIS,[41,5]],[120,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,120,-1,0,-1,0,0,0,0,0],
[TENSOR,[44,2]],[220,20,0,10,0,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-22,0,-2,0,-1,-1,0,1,1],[220,20,0,-5,0,0,0,0,0,5,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-22,0,-2,0,
E(33)+E(33)^2+E(33)^4+E(33)^8+E(33)^16+E(33)^17+E(33)^25+E(33)^29+E(33)^31
 +E(33)^32,E(33)^5+E(33)^7+E(33)^10+E(33)^13+E(33)^14+E(33)^19+E(33)^20
 +E(33)^23+E(33)^26+E(33)^28,0,-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16
 -E(33)^17-E(33)^25-E(33)^29-E(33)^31-E(33)^32,-E(33)^5-E(33)^7-E(33)^10
 -E(33)^13-E(33)^14-E(33)^19-E(33)^20-E(33)^23-E(33)^26-E(33)^28],
[GALOIS,[47,5]],[330,-30,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-33,0,3,0,0,0,1,0,0]],
[(45,46)(48,49),(11,12)(33,39)(34,37)(35,38)(36,40),( 6, 7, 9, 8)(13,15,16,14)
(17,19,20,18)(21,22,23,24)(25,27,28,26)(29,30,32,31)(33,38,36,34)
(35,40,37,39)]);
ARC("11+^(1+2):(5x2S4)","CAS",[rec(name:="j4n11",
permchars:=(),
permclasses:=(),
text:=[
"Maximal subgroup of sporadic Janko group j4.\n",
"Table received from Essen; fusion into j4 by O.Bonten and K.Lux\n",
"test: restricted characters decompose properly.\n",
""])]);
ALF("11+^(1+2):(5x2S4)","J4",[1,2,3,4,5,8,8,8,8,9,14,14,17,17,17,17,18,18,
18,18,28,28,28,28,30,31,31,30,42,42,42,42,54,53,53,54,53,53,54,54,19,20,
34,35,46,47,60,61,62],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("11+^(1+2):(5x2S4)",["J4N11"]);

MOT("2.HS.2N5",
[
"origin: Dixon's Algorithm,\n",
"Sylow 5 normalizer in 2.HS.2,\n",
"maximal subgroup of 2.HS.2,\n",
"table is sorted w.r. to normal series 2.5.5^2.8.2.2,\n",
"tests: 1.o.r., pow[2,5]"
],
[8000,8000,2000,2000,200,200,100,100,320,320,80,80,32,32,16,16,16,16,80,40,40,
160,160,40,40,40,20,20,80,40,40,80,40,40,40,40,40,40,40,16,16],
[,[1,1,3,3,5,5,7,7,1,1,3,3,10,10,13,13,14,14,9,11,11,2,2,6,6,1,7,7,23,25,25,
22,24,24,11,11,9,11,11,23,22],,,[1,2,1,2,1,2,1,2,9,10,9,10,13,14,15,16,17,18,
19,19,19,22,23,22,23,26,26,26,29,29,29,32,32,32,37,37,37,37,37,40,41]],
0,
[(35,36)(38,39),(30,31)(33,34),(27,28),(20,21)(27,28)(30,31)(33,34)
(35,39,36,38),(13,14)(15,17)(16,18)(22,23)(24,25)(29,32)(30,33)(31,34)(40,41),
(15,16)(17,18)],
["ConstructProj",[["HS.2N5",[]],["2.HS.2N5",[]]]]);
ALF("2.HS.2N5","HS.2N5",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,9,10,10,11,12,12,
13,13,14,14,15,16,16,17,18,18,19,20,20,21,21,22,23,23,24,25]);
ALF("2.HS.2N5","2.HS.2",[1,2,11,12,13,14,15,16,4,3,25,24,10,10,23,23,23,
23,8,32,33,5,5,26,26,35,46,45,38,51,50,38,50,51,54,55,36,53,52,38,38],[
"compatible with 5^(1+2):8:4 -> 2.HS"
]);
ALF("2.HS.2N5","5^(1+4):2^(1+4).5.4",[1,10,2,12,3,13,4,14,8,10,9,12,31,30,
45,43,44,42,11,15,16,31,30,39,38,29,34,33,42,52,50,43,51,53,16,16,11,15,
15,44,45],[
"fusion map determined by explicit computations from the groups"
]);
ALN("2.HS.2N5",["2.HS.2M9","HNN10A"]);

MOT("2^3.7.3",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,7]\n",
"Sylow 2 normalizer in sporadic Janko group J1"
],
[168,24,7,7,6,6,6,6],
[,[1,1,3,4,7,7,5,5],[1,2,4,3,1,2,1,2],,,,[1,2,1,1,5,6,7,8]],
[[1,1,1,1,1,1,1,1],[1,1,1,1,E(3),E(3),E(3)^2,E(3)^2],
[TENSOR,[2,2]],[3,3,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0],
[GALOIS,[4,3]],[7,-1,0,0,1,-1,1,-1],
[TENSOR,[6,2]],
[TENSOR,[6,3]]],
[(5,7)(6,8),(3,4)]);
ARC("2^3.7.3","CAS",[rec(name:="j1n2",
permchars:=(1,2)(4,5)(6,8),
permclasses:=(3,7,4,8,5),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ARC("2^3.7.3","tomfusion",rec(name:="2^3:7:3",map:=[1,2,6,6,3,5,3,5],text:=[
"fusion map is unique"
]));
ALF("2^3.7.3","J1",[1,2,7,7,3,6,3,6],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^3.7.3","L2(8).3",[1,2,4,4,6,8,7,9],[
"fusion map is unique up to table autom."
]);
ALN("2^3.7.3",["J1N2"]);

MOT("2^4:D8",
[
"origin: Ostermann, tests: 1.o.r., pow[2],\n",
"2nd power map determined only up to matrix automorphisms,\n",
"Sylow 2 normalizer in sporadic Mathieu group M22\n",
"Sylow 2 normalizer in sporadic Mathieu group M23"
],
[128,128,64,32,32,16,16,16,32,16,16,16,16,16,8,8,8],
[,[1,1,1,1,1,1,1,1,2,2,3,3,2,3,4,5,9]],
[[1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1],[1,1,1,1,1,-1,-1,1,1,-1,-1,1,-1,
-1,1,-1,1],[1,1,1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1],[1,1,1,1,1,-1,1,1,1,-1,
1,1,1,1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,-2,-2,0,0,0,2,0,0,0,-2,2,0,0,0],
[TENSOR,[9,2]],[2,2,2,-2,2,0,0,-2,-2,0,0,2,0,0,0,0,0],
[TENSOR,[11,1]],[2,2,2,2,-2,0,-2,0,-2,0,2,0,0,0,0,0,0],
[TENSOR,[13,1]],[4,4,-4,0,0,-2,0,0,0,2,0,0,0,0,0,0,0],
[TENSOR,[15,1]],[8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 4, 5)( 7, 8)(11,12)(15,16)]);
ARC("2^4:D8","CAS",[rec(name:="m22n2",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="m23n2",
permchars:=( 1, 5)( 2, 3)( 4, 8)( 6, 7)( 9,11)(10,12),
permclasses:=( 4, 5)( 6, 8)(10,12)(11,13),
text:="")]);
ALF("2^4:D8","s61p",[1,1,2,3,4,5,11,12,6,7,13,14,8,9,15,16,10]);
ALF("2^4:D8","2.A8",[1,2,3,3,3,3,3,3,4,4,9,9,4,9,9,9,10],[
"fusion map is unique"
]);
ALF("2^4:D8","LyN2",[1,2,3,5,5,7,11,11,4,8,16,16,6,13,19,19,17],[
"fusion map is unique"
]);
ALF("2^4:D8","M22",[1,2,2,2,2,2,2,2,4,4,5,5,5,4,4,5,10],[
"determined using that exactly one roots class of the central involution\n",
"fuses in 4B of M22; together with that, the map is unique up to table\n",
"automorphisms"
]);
ALF("2^4:D8","M23",[1,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,9],[
"fusion map is unique"
]);
ALF("2^4:D8","U4(3)",[1,2,2,2,2,2,2,2,7,7,8,8,8,7,8,8,15],[
"fusion map determined by the groups"
]);
ALN("2^4:D8",["2.A8N2","M22N2","M23N2","U4(3)N2"]);

MOT("2x(3^2.QD16)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Higman Sims group HS"
],
[288,288,32,32,24,24,36,16,16,8,8,36,12,12,16,16,16,16],
[,[1,1,1,1,1,1,7,3,3,3,3,7,7,7,9,9,9,9],[1,2,3,4,5,6,1,8,9,10,11,2,6,5,15,16,
17,18]],
[[1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1],[1,1,1,1,-1,-1,1,1,1,-1,-1,1,
-1,-1,1,1,1,1],[1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,1],[1,1,1,1,1,1,1,
1,1,-1,-1,1,1,1,-1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,2,0,0,2,-2,-2,0,0,2,0,0,0,0,0,0],
[TENSOR,[9,1]],[2,2,-2,-2,0,0,2,0,0,0,0,2,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[11,1]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[8,-8,0,0,-2,2,-1,0,0,0,0,1,-1,1,0,0,0,0],
[TENSOR,[15,3]],
[TENSOR,[15,1]],
[TENSOR,[15,2]]],
[(15,16)(17,18),(10,11)(15,17)(16,18),( 5, 6)(10,11)(13,14)]);
ARC("2x(3^2.QD16)","CAS",[rec(name:="hsn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALN("2x(3^2.QD16)",["HSN3"]);
ALF("2x(3^2.QD16)","HS",[1,3,2,3,2,3,4,6,7,7,7,11,11,12,15,15,16,16],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(1+2):8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Janko group J2"
],
[216,24,108,9,24,24,12,8,8,8,8,12,12],
[,[1,1,3,4,2,2,3,6,5,6,5,7,7],[1,2,1,1,6,5,2,9,8,11,10,5,6]],
[[1,-1,1,1,E(4),-E(4),-1,E(8)^3,E(8),-E(8)^3,-E(8),-E(4),E(4)],
[GALOIS,[1,5]],
[GALOIS,[1,3]],
[GALOIS,[1,7]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,3]],
[TENSOR,[1,4]],[6,2,-3,0,2*E(4),-2*E(4),-1,0,0,0,0,E(4),-E(4)],
[TENSOR,[9,5]],
[TENSOR,[9,3]],
[TENSOR,[9,1]],[8,0,8,-1,0,0,0,0,0,0,0,0,0]],
[( 5, 6)( 8, 9)(10,11)(12,13),( 5, 6)( 8,11)( 9,10)(12,13),( 8,10)( 9,11)]);
ARC("3^(1+2):8","CAS",[rec(name:="j2n3",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="3^1+2:8",
permchars:=( 1, 7, 2, 8)( 3, 5, 4, 6)( 9,12)(10,11),
permclasses:=( 2, 4, 3)( 5, 6)( 9,11,10),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ALF("3^(1+2):8","3^(1+2):SD16",[1,2,4,5,6,6,8,10,10,11,11,14,14],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):8","J2",[1,2,4,5,6,6,11,14,14,14,14,19,19],[
"fusion map is unique"
]);
ALF("3^(1+2):8","U3(3)",[1,2,3,4,5,6,8,12,11,12,11,14,13],[
"fusion map is unique up to table autom."
]);
ALN("3^(1+2):8",["J2N3","U3(3)N3","3^1+2:8"]);

MOT("3^(1+2):D8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M24,\n",
"Sylow 3 normalizer in sporadic Held group He,\n",
"5th maximal subgroup (novelty) in M12.2"
],
[216,24,12,12,108,18,18,12,12,6,6,12,12],
[,[1,1,1,1,5,6,7,2,5,6,7,9,9],[1,2,3,4,1,1,1,8,2,3,4,8,8]],
[[1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1],
[TENSOR,[1,1]],[1,1,-1,1,1,1,1,-1,1,-1,1,-1,-1],
[TENSOR,[1,3]],[2,-2,0,0,2,2,2,0,-2,0,0,0,0],[4,0,-2,0,4,1,-2,0,0,1,0,0,0],
[TENSOR,[6,3]],[4,0,0,-2,4,-2,1,0,0,0,1,0,0],
[TENSOR,[8,1]],[6,-2,0,0,-3,0,0,-2,1,0,0,1,1],
[TENSOR,[10,1]],[6,2,0,0,-3,0,0,0,-1,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11],
[TENSOR,[12,1]]],
[(12,13),( 3, 4)( 6, 7)(10,11)]);
ARC("3^(1+2):D8","CAS",[rec(name:="m24n3",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="hen3",
permchars:=( 1, 4, 2, 3)( 6, 9, 7, 8)(10,11),
permclasses:=(),
text:="")]);
ARC("3^(1+2):D8","tomfusion",rec(name:="3^(1+2)+:D8",map:=[1,2,3,4,5,7,6,8,
15,17,18,25,25],text:=[
"fusion map is unique up to table autom."
]));
ALF("3^(1+2):D8","M12.2",[1,3,3,13,4,4,5,14,9,9,16,20,21],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+2):D8","M24",[1,2,2,3,4,4,5,6,10,10,11,17,17],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","He",[1,2,2,3,4,4,5,6,10,10,11,19,19],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","L3(3).2",[1,2,2,10,3,3,4,11,6,6,12,14,15],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","3.A6.2_1",[1,3,12,13,2,5,6,7,4,15,16,8,8],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","3.A7.2",[1,3,16,17,2,5,6,7,4,19,20,8,8],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","2^6:3^(1+2).D8",[1,10,19,25,5,6,8,15,14,23,29,17,18],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","3^(1+2):SD16",[1,2,3,3,4,5,5,6,8,9,9,14,14],[
"fusion map is unique"
]);
ALF("3^(1+2):D8","2F4(2)'",[1,3,3,3,4,4,4,5,9,9,9,15,16],[
"fusion map is unique up to table aut."
]);
ALN("3^(1+2):D8",["M24N3","HeN3","2F4(2)'N3","3.A6.2_1N3","3.A7.2N3"]);

MOT("3^(1+2):SD16",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Rudvalis group Ru,"
],
[432,48,12,216,18,24,12,24,6,8,8,12,12,12],
[,[1,1,1,4,5,2,2,4,5,6,6,8,8,8],[1,2,3,1,1,6,7,2,3,10,11,7,7,6]],
[[1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1],[1,1,-1,1,1,1,-1,1,-1,1,1,-1,-1,1],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,-2,0,2,2,0,0,-2,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0],
[TENSOR,[5,1]],[2,2,0,2,2,-2,0,2,0,0,0,0,0,-2],[6,-2,0,-3,0,-2,0,1,0,0,0,
E(3)-E(3)^2,-E(3)+E(3)^2,1],
[TENSOR,[8,1]],[6,-2,0,-3,0,2,2,1,0,0,0,-1,-1,-1],
[TENSOR,[10,1]],[8,0,2,8,-1,0,0,0,-1,0,0,0,0,0],
[TENSOR,[12,2]],[12,4,0,-6,0,0,0,-2,0,0,0,0,0,0]],
[(12,13),(10,11)]);
ARC("3^(1+2):SD16","CAS",[rec(name:="run3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^(1+2):SD16","G2(4)",[1,2,3,4,5,6,7,13,14,16,16,23,24,22],[
"fusion map determined up to table aut. by the fact that\n",
"the order 12 elements are not all conjugate in G2(4)"
]);
ALF("3^(1+2):SD16","J2.2",[1,2,17,4,5,6,18,9,20,12,12,23,23,15],[
"fusion map determined by the fact that\n",
"the order 12 elements are not all conjugate in J2.2"
]);
ALF("3^(1+2):SD16","Ru",[1,2,2,4,4,5,6,11,11,13,13,19,19,18],[
"fusion map is unique"
]);
ALF("3^(1+2):SD16","U3(3).2",[1,2,11,3,4,5,12,7,13,9,9,15,16,10],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+2):SD16","2F4(2)'.2",[1,3,3,4,4,5,20,9,9,23,23,24,25,14],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+2):SD16","3.M22.2",[1,3,23,2,5,6,8,4,27,28,28,9,9,7],[
"fusion map is unique"
]);
ALN("3^(1+2):SD16",["G2(4)N3","J2.2N3","RuN3"]);

MOT("3^2.3^(1+2):8",
[
"origin: CAS library,\n",
"Sylow 3 normalizer in sporadic Janko group J3,\n",
"maximal subgroup of J3,\n",
"tests: 1.o.r., pow[2,3]"
],
[1944,243,108,27,27,27,24,12,24,12,24,12,8,8,8,8],
[,[1,2,3,5,6,4,1,3,7,8,7,8,9,11,9,11],[1,1,1,2,2,2,7,7,11,11,9,9,14,13,16,
15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,-1,-1,-1,-1,E(4),-E(4),E(4),-E(4)],
[TENSOR,[2,3]],[1,1,1,1,1,1,-1,-1,E(4),E(4),-E(4),-E(4),E(8),E(8)^3,-E(8),
-E(8)^3],
[TENSOR,[5,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[6,6,-3,0,0,0,-2,1,2,-1,2,-1,0,0,0,0],
[TENSOR,[9,3]],
[TENSOR,[9,5]],
[TENSOR,[9,6]],[8,8,8,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[24,-3,0,-2*E(9)^2-E(9)^4
 -E(9)^5-2*E(9)^7,E(9)^2-E(9)^4-E(9)^5+E(9)^7,E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,
0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,4]],
[GALOIS,[14,2]]],
[( 9,11)(10,12)(13,14)(15,16),( 9,11)(10,12)(13,16)(14,15),(4,5,6),(4,6,5),
(13,15)(14,16)]);
ARC("3^2.3^(1+2):8","CAS",[rec(name:="j3n3",
permchars:=( 1, 2)( 3, 7)( 4, 8, 5)( 9,10)(14,16),
permclasses:=( 2, 3, 4,12,15,10,16,11, 6,14, 9, 5,13, 8, 7),
text:=""),rec(name:="j3m7",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("3^2.3^(1+2):8","tomfusion",rec(name:="3^2.3^(1+2):8",map:=[1,3,4,11,
11,11,2,6,5,12,5,12,8,8,8,8],text:=[
"fusion map is unique"
]));
ALF("3^2.3^(1+2):8","3^2.3^(1+2):8.2",[1,2,3,4,5,6,7,8,9,10,9,10,11,11,12,
12],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^2.3^(1+2):8","J3",[1,4,3,10,11,12,2,8,5,15,5,15,9,9,9,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("3^2.3^(1+2):8",["J3N3"]);

MOT("3^2:Q8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M22"
],
[72,8,9,4,4,4],
[,[1,1,3,2,2,2],[1,2,1,4,5,6]],
[[1,1,1,-1,-1,1],[1,1,1,-1,1,-1],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,2,0,0,0],[8,0,-1,0,0,0]],
[(5,6),(4,5)]);
ARC("3^2:Q8","projectives",["3^(1+2)_+:Q8",[[3,-1,0,-1,-1,1],[6,2,0,0,0,0]],
]);
ARC("3^2:Q8","CAS",[rec(name:="m22n3",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("3^2:Q8","tomfusion",rec(name:="3^2:Q8",map:=[1,2,3,4,5,6],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^2:Q8","A6.2_3",[1,2,3,4,6,6],[
"fusion map is unique up to table autom."
]);
ALF("3^2:Q8","M22",[1,2,3,4,5,5],[
"fusion map determined up to table automorphisms\n",
"by factorization through M10"
]);
ALF("3^2:Q8","L3(4)",[1,2,3,4,5,6],[
"fusion map determined by the fact that the class of subgroups\n",
"is invariant under the automorphism group"
]);
ALF("3^2:Q8","L3(7)",[1,2,3,4,4,4],[
"fusion map is unique"
]);
ALF("3^2:Q8","U3(11)",[1,2,3,6,6,6],[
"fusion map is unique"
]);
ALF("3^2:Q8","U3(5)",[1,2,3,4,4,4],[
"fusion map is unique"
]);
ALF("3^2:Q8","3^2:Q8.2",[1,2,4,5,6,6],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^2:Q8","3^2:2A4",[1,3,2,4,4,4],[
"fusion map is unique"
]);
ALN("3^2:Q8",["L3(4)N3","M22N3","U3(5)N3"]);

MOT("3^2:Q8.2",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M11,\n",
"maximal subgroup of M11,\n",
"Sylow 3 normalizer in sporadic Mathieu group M23,\n",
"Sylow 3 normalizer in M22.2"
],
[144,16,12,18,8,4,6,8,8],
[,[1,1,1,4,2,2,4,5,5],[1,2,3,1,5,6,3,8,9]],
[[1,1,1,1,1,-1,1,-1,-1],[1,1,-1,1,1,1,-1,-1,-1],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,0,2,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[5,1]],[2,2,0,2,-2,0,0,0,0],[8,0,-2,-1,0,0,1,0,0],
[TENSOR,[8,2]]],
[(8,9)]);
ARC("3^2:Q8.2","CAS",[rec(name:="m11n3",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="m23n3",
permchars:=(2,3),
permclasses:=(),
text:="")]);
ARC("3^2:Q8.2","tomfusion",rec(name:="M9:2",map:=[1,3,2,4,6,7,10,13,13],
text:=[
"fusion map is unique"
]));
ALF("3^2:Q8.2","A6.2^2",[1,2,6,3,4,12,8,10,10],[
"fusion map is unique"
]);
ALF("3^2:Q8.2","L3(4).2_2",[1,2,9,3,4,5,11,12,12],[
"fusion map is unique"
]);
ALF("3^2:Q8.2","L3(4).2_3",[1,2,9,3,4,5,10,11,11],[
"fusion map uniquely determined by Brauer tables"
]);
ALF("3^2:Q8.2","M11",[1,2,2,3,4,4,6,7,8],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^2:Q8.2","M23",[1,2,2,3,4,4,6,9,9],[
"fusion map is unique"
]);
ALF("3^2:Q8.2","M22.2",[1,2,12,3,4,5,16,17,17],[
"determined by the embedding of 3^2:Q8 = M22N3"
]);
ALN("3^2:Q8.2",["3^2:SD16","M11N3","M22.2N3","M23N3"]);

MOT("3^4:(3^2:Q8)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic McLaughlin group McL,"
],
0,
0,
0,
0,
["ConstructPermuted",["3^4.3^2.Q8"],(2,3,5,6,7,8,9,16,10,17,18,19,20,21,11,14,
15,12),(1,4)(2,3)(6,10,7,9)(13,17,15,19,14,18)]);
ARC("3^4:(3^2:Q8)","CAS",[rec(name:="mcn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^4:(3^2:Q8)","McL",[1,2,3,3,4,4,4,4,4,5,5,5,8,8,9,13,14,18,18,18,18],[
"fusion map is unique up to table autom."
]);
ALF("3^4:(3^2:Q8)","McL.2N3",[1,11,2,6,3,7,4,5,5,16,17,12,14,13,15,8,8,18,
18,19,19]);
ALN("3^4:(3^2:Q8)",["McLN3"]);

MOT("3^4:2^(1+4)D10",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 3 normalizer in sporadic O'Nan group ON,\n",
"maximal subgroup of ON"
],
[25920,320,288,324,144,32,32,16,8,10,10,36,8,8,10,10,36,36],
[,[1,1,1,4,3,2,2,3,2,11,10,4,6,7,10,11,12,12],[1,2,3,1,5,6,7,8,9,11,10,3,13,
14,16,15,5,5],,[1,2,3,4,5,6,7,8,9,1,1,12,13,14,2,2,17,18]],
[[1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,-1],
[TENSOR,[1,1]],[2,2,2,2,0,2,2,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,2,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0],
[GALOIS,[3,2]],[4,-4,0,4,2,0,0,-2,0,-1,-1,0,0,0,1,1,2,2],
[TENSOR,[5,1]],[5,5,-3,5,1,1,1,1,1,0,0,-3,-1,-1,0,0,1,1],[5,5,1,5,-1,1,-3,-1,
1,0,0,1,-1,1,0,0,-1,-1],[5,5,1,5,1,-3,1,1,-1,0,0,1,-1,1,0,0,1,1],
[TENSOR,[7,1]],
[TENSOR,[8,1]],
[TENSOR,[9,1]],[8,-8,0,8,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,0],
[GALOIS,[13,2]],[80,0,8,-1,8,0,0,0,0,0,0,-1,0,0,0,0,-1,-1],
[TENSOR,[15,1]],[80,0,-8,-1,0,0,0,0,0,0,0,1,0,0,0,0,-3*E(4),3*E(4)],
[TENSOR,[17,1]]],
[(17,18),(10,11)(15,16),( 6, 7)(13,14)]);
ARC("3^4:2^(1+4)D10","CAS",[rec(name:="onn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^4:2^(1+4)D10","ON",[1,2,2,3,4,5,5,5,5,6,6,7,10,11,12,12,14,14],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^4:2^(1+4)D10","3^4:2^(1+4).(5:4)",[1,3,5,2,9,4,4,10,11,7,7,6,12,12,
8,8,13,14]);
ALN("3^4:2^(1+4)D10",["ONN3"]);

MOT("3^4:2^(1+4).(5:4)",
[
"Sylow 3 normalizer in ON.2,\n",
"5th maximal subgroup of ON.2,\n,",
"origin: Dixon's Algorithm"
],
[51840,648,640,32,576,72,10,10,288,32,16,8,72,72,48,48,8,24,24,48,48,8,24,24],
[,[1,2,1,3,1,2,7,7,5,5,3,4,6,6,9,9,11,14,14,9,9,11,13,13],[1,1,3,4,5,5,7,8,9,
10,11,12,9,9,20,21,22,20,21,15,16,17,15,16],,[1,2,3,4,5,6,1,3,9,10,11,12,13,14
,16,15,17,19,18,21,20,22,24,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,E(4),E(4),E(4),E(4),E(4),-E(4),-E(4),-E(4),-E(4),-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[4,4,4,4,4,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,1,
-3,-3,0,0,1,1,1,-1,1,1,1,1,-1,1,1,1,1,-1,1,1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],[10,10,10,-2,2,2,0,0,2,2,-2,0,2,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[10,2]],[4,4,-4,0,0,0,-1,1,-2,2,0,0,-2,-2,E(8)-E(8)^3,-E(8)+E(8)^3,0,
E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,-E(8)+E(8)^3,E(8)-E(8)^3],
[TENSOR,[12,2]],
[TENSOR,[12,3]],
[TENSOR,[12,4]],[16,16,-16,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,-1
,0,0,8,-1,0,0,8,0,0,0,-1,-1,2,2,0,-1,-1,2,2,0,-1,-1],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[80,-1,0,0,-8,1,0,0,0,0,0,0,-3*E(4),3*E(4),2*E(8),-2*E(8),0,
-E(8),E(8),2*E(8)^3,-2*E(8)^3,0,-E(8)^3,E(8)^3],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]]],
[(15,16)(18,19)(20,21)(23,24),(13,14)(15,21)(16,20)(17,22)(18,24)(19,23)]);
ALF("3^4:2^(1+4).(5:4)","ON.2",[1,3,2,5,2,7,6,11,4,5,5,10,13,13,28,29,30,
35,36,29,28,30,36,35],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^4:2^(1+4).(5:4)",["ON.2N3"]);

MOT("3^5:(3^2:SD16)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Suzuki group Suz,"
],
[34992,432,324,8748,8748,1944,972,972,486,486,162,81,24,12,324,324,216,108,
108,108,108,108,108,108,108,108,108,54,54,18,8,8,54,54,12,12,12,18,18],
[,[1,1,1,4,5,6,8,7,9,10,11,12,2,2,5,5,6,8,7,8,7,6,6,4,5,8,7,9,10,11,13,13,34,
33,24,24,17,33,34],[1,2,3,1,1,1,1,1,1,1,1,1,13,14,3,3,2,3,3,2,2,3,3,2,2,3,3,2,
3,3,31,32,5,5,14,14,13,15,16]],
[[1,1,-1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,-1,
-1,1,1,1,1,1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,-1,-1,1,1,-1,-1,1,1,1],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,-2,0,2,2,2,2,2,2,2,2,2,0,0,0,0,-2,0,0,-2,-2,0,0,-2,-2,0,0,
-2,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,2,2,0,0,0,0,0],
[TENSOR,[5,1]],[2,2,2,2,2,-1,-1,-1,-1,2,2,2,2,0,2,2,-1,-1,-1,-1,-1,-1,-1,2,2,
-1,-1,-1,2,2,0,0,-1,-1,0,0,-1,-1,-1],
[TENSOR,[7,1]],[2,2,0,2,2,-1,-1,-1,-1,2,2,2,-2,0,0,0,-1,-E(3)+E(3)^2,
E(3)-E(3)^2,-1,-1,E(3)-E(3)^2,-E(3)+E(3)^2,2,2,-E(3)+E(3)^2,E(3)-E(3)^2,-1,0,
0,0,0,-1,-1,0,0,1,-E(3)+E(3)^2,E(3)-E(3)^2],
[TENSOR,[9,1]],[2,2,0,2,2,2,2,2,2,2,2,2,-2,0,0,0,2,0,0,2,2,0,0,2,2,0,0,2,0,0,
0,0,2,2,0,0,-2,0,0],[4,-4,0,4,4,-2,-2,-2,-2,4,4,4,0,0,0,0,2,0,0,2,2,0,0,-4,-4,
0,0,2,0,0,0,0,-2,-2,0,0,0,0,0],[8,0,-2,8,8,8,8,8,8,8,-1,-1,0,0,-2,-2,0,-2,-2,
0,0,-2,-2,0,0,-2,-2,0,-2,1,0,0,-1,-1,0,0,0,1,1],
[TENSOR,[13,1]],[8,0,2,8,8,-4,-4,-4,-4,8,-1,-1,0,0,2,2,0,2*E(3)^2,2*E(3),0,0,
2*E(3),2*E(3)^2,0,0,2*E(3)^2,2*E(3),0,2,-1,0,0,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,0,
0,0,-E(3)^2,-E(3)],
[TENSOR,[15,1]],
[GALOIS,[15,2]],
[TENSOR,[17,1]],[24,0,-6,24,24,0,0,0,0,-3,6,-3,0,0,-6,-6,0,0,0,0,0,0,0,0,0,0,
0,0,3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[19,1]],[36,-4,0,9,-18,-12,6,6,-3,0,0,0,0,0,0,0,-4,0,0,2,2,0,0,-1,2,0,
0,-1,0,0,0,0,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0],
[TENSOR,[21,2]],[36,4,0,9,-18,-12,6,6,-3,0,0,0,0,2,0,0,4,0,0,-2,-2,0,0,1,-2,0,
0,1,0,0,0,0,0,0,-1,-1,0,0,0],
[TENSOR,[23,2]],[36,4,6,-18,9,12,3,3,-6,0,0,0,0,0,-3,-3,4,-3,-3,1,1,0,0,-2,1,
3,3,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,1]],[36,-4,0,-18,9,12,3,3,-6,0,0,0,0,0,-3*E(3)+3*E(3)^2,
3*E(3)-3*E(3)^2,-4,-E(3)+E(3)^2,E(3)-E(3)^2,-1,-1,-2*E(3)+2*E(3)^2,
2*E(3)-2*E(3)^2,2,-1,-E(3)+E(3)^2,E(3)-E(3)^2,2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,1]],[36,-4,0,-18,9,-6,-3*E(3)+6*E(3)^2,6*E(3)-3*E(3)^2,3,0,0,0,0,
0,3*E(3)-3*E(3)^2,-3*E(3)+3*E(3)^2,2,E(3)+2*E(3)^2,2*E(3)+E(3)^2,
E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-4*E(3)-2*E(3)^2,-2*E(3)-4*E(3)^2,2,-1,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,-1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,1]],
[GALOIS,[30,2]],
[TENSOR,[31,1]],[36,4,-6,-18,9,-6,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,3,0,0,0,0,
0,3,3,-2,3*E(3)^2,3*E(3),2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,-2,1,-3*E(3)^2,
-3*E(3),1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,1]],
[GALOIS,[34,2]],
[TENSOR,[35,1]],[48,0,0,48,48,0,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[72,8,0,18,-36,12,-6,-6,3,0,0,0,0,0,0,0,-4,0,0,2,2,0,0,
2,-4,0,0,-1,0,0,0,0,0,0,0,0,0,0,0],[72,-8,0,18,-36,12,-6,-6,3,0,0,0,0,0,0,0,4,
0,0,-2,-2,0,0,-2,4,0,0,1,0,0,0,0,0,0,0,0,0,0,0]],
[(35,36),(31,32),(31,32)(35,36),( 7, 8)(15,16)(18,19)(20,21)(22,23)(26,27)
(33,34)(35,36)(38,39),( 7, 8)(15,16)(18,19)(20,21)(22,23)(26,27)(33,34)
(38,39)]);
ARC("3^5:(3^2:SD16)","CAS",[rec(name:="suzn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^5:(3^2:SD16)","Suz",[1,2,2,4,5,4,5,5,5,5,5,6,9,9,14,15,13,16,16,14,
15,13,13,13,16,15,14,16,16,16,21,21,23,22,29,29,29,38,39],[
"determined up to table automorphisms by factorization through 3^5:M11"
]);
ALF("3^5:(3^2:SD16)","LyN3",[1,2,3,7,8,9,11,11,10,12,13,14,17,18,20,20,19,
28,28,24,24,29,29,21,22,23,23,25,27,34,38,39,40,40,48,48,47,49,49],[
"fusion map is unique up to table aut."
]);
ALN("3^5:(3^2:SD16)",["SuzN3"]);

MOT("4^3.D8",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic O'Nan group ON,"
],
[512,512,256,128,32,32,32,16,256,256,128,128,128,64,64,64,64,64,32,32,32,16,
32,32,16,16,16,16,16,16,16,16],
[,[1,1,1,1,1,1,1,1,2,2,3,2,3,4,3,4,4,4,2,2,2,3,9,9,12,12,11,11,23,23,24,24]],
[[1,1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,1,
1],[1,1,1,1,-1,1,-1,1,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,
1,1],[1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,-1,1,1,
-1,-1],[1,1,1,1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,
1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,2,0,0,2,0,2,2,2,2,2,-2,2,-2,-2,-2,0,0,2,0,-2,-2,0,0,0,0,
0,0,0,0],
[TENSOR,[9,1]],[2,2,2,-2,0,0,-2,0,-2,-2,2,2,2,0,-2,0,0,0,0,0,2,0,0,0,0,0,0,0,
-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3],
[TENSOR,[11,3]],
[TENSOR,[11,1]],
[TENSOR,[11,5]],[2,2,2,2,0,2,0,0,2,2,-2,2,-2,0,-2,0,0,0,0,2,0,0,-2,2,-2,0,0,0,
0,0,0,0],
[TENSOR,[15,1]],[2,2,2,2,-2,0,0,0,2,2,-2,2,-2,0,-2,0,0,0,-2,0,0,0,2,-2,0,2,0,
0,0,0,0,0],
[TENSOR,[17,2]],[4,4,-4,0,-2,2,0,0,4,-4,0,0,0,-2,0,2,2,-2,2,-2,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[19,5]],
[TENSOR,[19,1]],
[TENSOR,[19,2]],[4,4,4,-4,0,0,0,0,-4,-4,-4,4,-4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[4,4,4,-4,0,0,0,-2,4,4,0,-4,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[24,1]],[4,4,4,4,0,0,0,0,-4,-4,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,
0,0,0,0],
[TENSOR,[26,2]],[8,-8,0,0,0,0,0,0,0,0,4,0,-4,-4,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],
[TENSOR,[28,1]],[8,8,-8,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[8,-8,0,0,0,0,0,0,0,0,-4,0,4,0,0,-4*E(4),4*E(4),0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[31,1]]],
[(29,30)(31,32),(27,28),(16,17),(16,17)(29,30)(31,32),(14,18),( 5, 6)(19,20)
(23,24)(25,26)(29,31)(30,32)]);
ARC("4^3.D8","CAS",[rec(name:="onn2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("4^3.D8","ON",[1,2,2,2,2,2,2,2,5,4,5,5,4,4,5,5,5,5,5,5,5,5,10,11,11,
10,10,11,18,19,20,21],[
"fusion map is unique up to table autom."
]);
ALF("4^3.D8","ON.2N2",[1,2,3,5,18,18,16,22,7,6,9,4,10,12,8,11,11,13,19,19,
15,21,14,14,17,17,20,20,23,24,23,24]);
ALN("4^3.D8",["ONN2"]);

MOT("5^(1+2):(24:2)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Conway group Co3,\n",
"10th maximal subgroup of McL.2"
],
[6000,240,40,120,48,48,40,1500,50,120,24,24,8,8,60,10,24,24,30,20,20,24,24,24,
24,30],
[,[1,1,1,4,2,2,2,8,9,4,6,5,5,6,8,9,10,10,19,15,15,18,17,18,17,19],[1,2,3,1,6,
5,7,8,9,2,12,11,14,13,15,16,5,6,8,20,21,11,12,11,12,15],,[1,2,3,4,5,6,7,1,1,
10,11,12,13,14,2,3,17,18,4,7,7,22,23,24,25,10]],
[[1,1,-1,1,-1,-1,1,1,1,1,E(4),-E(4),-E(4),E(4),1,-1,-1,-1,1,1,1,-E(4),E(4),
-E(4),E(4),1],[1,1,1,1,-1,-1,-1,1,1,1,-E(4),E(4),-E(4),E(4),1,1,-1,-1,1,-1,-1,
E(4),-E(4),E(4),-E(4),1],
[GALOIS,[1,3]],
[GALOIS,[2,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,3]],
[TENSOR,[1,4]],[2,2,0,-1,2,2,0,2,2,-1,-2,-2,0,0,2,0,-1,-1,-1,0,0,1,1,1,1,-1],
[TENSOR,[9,5]],
[TENSOR,[9,1]],
[TENSOR,[9,2]],[2,-2,0,2,-2*E(4),2*E(4),0,2,2,-2,0,0,0,0,-2,0,2*E(4),-2*E(4),
2,0,0,0,0,0,0,-2],[2,-2,0,-1,-2*E(4),2*E(4),0,2,2,1,0,0,0,0,-2,0,-E(4),E(4),
-1,0,0,-E(24)+E(24)^17,-E(24)^11+E(24)^19,E(24)-E(24)^17,E(24)^11-E(24)^19,1],
[TENSOR,[14,5]],
[TENSOR,[13,1]],
[TENSOR,[14,2]],
[TENSOR,[14,1]],[20,-4,0,-4,0,0,0,-5,0,-4,0,0,0,0,1,0,0,0,1,
E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,1],
[TENSOR,[19,2]],[20,4,0,-4,0,0,-4,-5,0,4,0,0,0,0,-1,0,0,0,1,1,1,0,0,0,0,-1],
[TENSOR,[21,2]],[24,0,4,0,0,0,0,24,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[23,1]],[40,-8,0,4,0,0,0,-10,0,4,0,0,0,0,2,0,0,0,-1,0,0,0,0,0,0,-1],[
40,8,0,4,0,0,0,-10,0,-4,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,1]],
[(22,24)(23,25),(20,21),( 5, 6)(11,12)(13,14)(17,18)(20,21)(22,23)(24,25),
( 5, 6)(11,12)(13,14)(17,18)(20,21)(22,25)(23,24),( 5, 6)(11,12)(13,14)(17,18)
(22,23)(24,25)]);
ARC("5^(1+2):(24:2)","CAS",[rec(name:="c3n5",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("5^(1+2):(24:2)","tomfusion",rec(name:="5^(1+2)+:3:8.2",map:=[1,2,3,4,
6,6,5,8,9,10,12,12,13,13,15,18,22,22,23,28,28,31,31,31,31,35],text:=[
"fusion map is unique"
]));
ALF("5^(1+2):(24:2)","Co3",[1,2,3,4,8,8,7,9,10,11,17,17,19,19,22,23,27,27,30,
33,34,40,40,40,40,42],[
"fusion map determined up to table autom. by Brauer tables,\n",
"the representative factors through McL.2"
]);
ALF("5^(1+2):(24:2)","McL.2",[1,2,20,3,5,5,21,6,7,8,23,23,11,11,13,25,16,16,
18,28,29,32,32,33,33,19],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+2):(24:2)","U3(5).3.2",[1,2,22,11,4,4,23,5,6,13,9,9,25,25,10,26,15,
15,16,28,29,19,20,20,19,21],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+2):(24:2)",["Co3N5","McL.2N5","U3(5).3.2N5"]);

MOT("5^(1+2):(8.2)",
[
"origin: Dixon's algorithm,\n",
"maximal subgroup of U3(5).2,\n",
"Sylow 5 normalizer in sporadic Higman Sims group HS,\n",
"Sylow 5 normalizer in U3(5).2,\n",
"table is sorted w.r. to normal series 5.5^2.8.2,\n",
"2nd power map determined only up to matrix automorphisms,\n",
"tests: 1.o.r., pow[2,5]"
],
[2000,500,50,25,80,20,16,16,8,8,8,8,40,20,20,40,10],
[,[1,2,3,4,1,2,5,5,7,8,7,8,5,6,6,1,3],,,[1,1,1,1,5,5,7,8,9,10,11,12,13,13,13,
16,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1],[1,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[1,1,1,1,1,1,-1,-1,-E(4),E(4),-E(4),E(4),1,1,1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,2,-2,-2,2*E(4),-2*E(4),0,0,0,0,0,0,0,0,0],
[TENSOR,[9,5]],[8,8,3,-2,0,0,0,0,0,0,0,0,0,0,0,-4,1],
[TENSOR,[11,2]],[16,16,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,-5,0,0,4,-1,0,0,0,
0,0,0,-4,1,1,0,0],
[TENSOR,[14,2]],[20,-5,0,0,-4,1,0,0,0,0,0,0,0,-E(20)-E(20)^9+E(20)^13+E(20)^17
 ,E(20)+E(20)^9-E(20)^13-E(20)^17,0,0],
[TENSOR,[16,2]]],
[(14,15),( 9,11)(10,12),( 7, 8)( 9,10)(11,12)(14,15),( 7, 8)( 9,10)(11,12)]);
ARC("5^(1+2):(8.2)","CAS",[rec(name:="hsn5",
permchars:=(1,4,3,7,2,8,6),
permclasses:=( 2, 7, 5)( 3, 8, 6,14,16)( 4, 9,10,11,12,13)(15,17),
text:="origin: Ostermann")]);
ARC("5^(1+2):(8.2)","tomfusion",rec(name:="5^(1+2)+:8:2",map:=[1,7,8,9,2,16,5,
5,10,10,12,12,4,23,23,3,18],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("5^(1+2):(8.2)","U3(5).2",[1,5,6,7,2,11,4,4,10,10,15,15,13,18,19,12,
16],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+2):(8.2)","HS",[1,8,9,10,2,17,7,7,15,15,16,16,5,23,24,3,18],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+2):(8.2)","HS.2N5",[1,2,3,4,5,6,7,8,9,10,9,10,11,12,12,13,14],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+2):(8.2)",["5^(1+2):8:2","HSN5","U3(5).2N5"]);

MOT("5^(1+2):3:8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic McLaughlin group McL,\n",
"maximal subgroup of McL"
],
[3000,120,60,24,24,750,25,60,8,8,8,8,30,12,12,30,30,30,30],
[,[1,1,3,2,2,6,7,3,4,5,4,5,6,8,8,16,17,16,17],[1,2,1,5,4,6,7,2,10,9,12,11,13,
5,4,6,6,13,13],,[1,2,3,4,5,1,1,8,11,12,9,10,2,14,15,3,3,8,8]],
[[1,-1,1,E(4),-E(4),1,1,-1,-E(8),-E(8)^3,E(8),E(8)^3,-1,E(4),-E(4),1,1,-1,-1],
[GALOIS,[1,5]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,
-1,-1,1,1,1,1,1,1,1],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,6]],
[TENSOR,[1,5]],[2,2,-1,2,2,2,2,-1,0,0,0,0,2,-1,-1,-1,-1,-1,-1],
[TENSOR,[9,5]],
[TENSOR,[9,7]],
[TENSOR,[9,1]],[20,4,2,0,0,-5,0,-2,0,0,0,0,-1,0,0,-E(15)^7-E(15)^11-E(15)^13
 -E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
E(15)+E(15)^2+E(15)^4+E(15)^8],
[GALOIS,[13,7]],[20,4,-4,0,0,-5,0,4,0,0,0,0,-1,0,0,1,1,-1,-1],
[TENSOR,[13,1]],
[TENSOR,[14,1]],
[TENSOR,[15,1]],[24,0,0,0,0,24,-1,0,0,0,0,0,0,0,0,0,0,0,0]],
[(16,17)(18,19),( 4, 5)( 9,10)(11,12)(14,15),( 4, 5)( 9,12)(10,11)(14,15),
( 9,11)(10,12)]);
ARC("5^(1+2):3:8","CAS",[rec(name:="mcn5",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("5^(1+2):3:8","tomfusion",rec(name:="5^(1+2)+:3:8",map:=[1,2,3,4,4,5,
6,7,8,8,8,8,9,11,11,12,12,17,17],text:=[
"fusion map is unique"
]));
ALF("5^(1+2):3:8","McL",[1,2,3,5,5,6,7,8,12,12,12,12,15,18,18,21,22,23,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5^(1+2):3:8","5^(1+2):(24:2)",[1,2,4,5,6,8,9,10,13,14,13,14,15,18,17,
19,19,26,26]);
ALN("5^(1+2):3:8",["McLN5"]);

MOT("5^(1+2):4S4",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5],\n",
"Sylow 5 normalizer in sporadic Conway group Co2,\n",
"9th maximal subgroup of Th"
],
[12000,480,80,60,96,96,80,80,80,16,16,3000,100,60,8,8,120,20,12,12,30,30,20,
20,20,30,30],
[,[1,1,1,4,2,2,3,3,2,3,3,12,13,4,5,6,12,13,14,14,21,22,18,18,17,22,21],[1,2,3,
1,6,5,8,7,9,11,10,12,13,2,16,15,17,18,5,6,12,12,24,23,25,17,17],,[1,2,3,4,5,6,
7,8,9,10,11,1,1,14,15,16,2,3,19,20,4,4,8,7,9,14,14]],
[[1,1,-1,1,-1,-1,E(4),-E(4),1,-E(4),E(4),1,1,1,-E(4),E(4),1,-1,-1,-1,1,1,
-E(4),E(4),1,1,1],
[GALOIS,[1,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,-2,0,-1,2*E(4),-2*E(4),1+E(4),1-E(4),0,-1+E(4),-1-E(4),2,2,
1,0,0,-2,0,E(4),-E(4),-1,-1,1-E(4),1+E(4),0,1,1],
[TENSOR,[5,3]],
[TENSOR,[5,2]],
[TENSOR,[5,1]],[2,2,2,-1,2,2,0,0,2,0,0,2,2,-1,0,0,2,2,-1,-1,-1,-1,0,0,2,-1,
-1],
[TENSOR,[9,1]],[3,3,1,0,-3,-3,E(4),-E(4),-1,-E(4),E(4),3,3,0,E(4),-E(4),3,1,0,
0,0,0,-E(4),E(4),-1,0,0],
[TENSOR,[11,3]],
[TENSOR,[11,2]],
[TENSOR,[11,1]],[4,-4,0,1,-4*E(4),4*E(4),0,0,0,0,0,4,4,-1,0,0,-4,0,E(4),-E(4),
1,1,0,0,0,-1,-1],
[TENSOR,[15,1]],[20,4,0,2,0,0,0,0,-4,0,0,-5,0,-2,0,0,-1,0,0,0,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,1,
E(15)+E(15)^2+E(15)^4+E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14],
[GALOIS,[17,7]],[20,4,0,-4,0,0,0,0,-4,0,0,-5,0,4,0,0,-1,0,0,0,1,1,0,0,1,-1,
-1],[24,0,-4,0,0,0,4*E(4),-4*E(4),0,0,0,24,-1,0,0,0,0,1,0,0,0,0,E(4),-E(4),0,
0,0],
[TENSOR,[20,3]],
[TENSOR,[20,2]],
[TENSOR,[20,1]],[40,-8,0,-2,0,0,0,0,0,0,0,-10,0,-2,0,0,2,0,0,0,
E(15)^7+E(15)^11+E(15)^13+E(15)^14,E(15)+E(15)^2+E(15)^4+E(15)^8,0,0,0,
E(15)+E(15)^2+E(15)^4+E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14],
[GALOIS,[24,7]],[40,-8,0,4,0,0,0,0,0,0,0,-10,0,4,0,0,2,0,0,0,-1,-1,0,0,0,-1,
-1],[60,12,0,0,0,0,0,0,4,0,0,-15,0,0,0,0,-3,0,0,0,0,0,0,0,-1,0,0]],
[(21,22)(26,27),( 5, 6)( 7, 8)(10,11)(15,16)(19,20)(23,24)]);
ARC("5^(1+2):4S4","CAS",[rec(name:="5^1+2:4s4",
permchars:=(),
permclasses:=(),
text:=[
"origin: CAS library,\n",
"Maximal subgroup of sporadic simple Conway group c2.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly."]),rec(name:="co2n5",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("5^(1+2):4S4","Co2",[1,3,4,5,11,11,13,13,8,13,13,14,15,16,28,28,30,32,
40,40,46,47,52,52,51,60,59],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5^(1+2):4S4","Th",[1,2,2,5,7,7,7,7,7,7,7,8,8,9,14,14,18,18,22,22,25,
26,30,30,30,41,40],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+2):4S4",["Co2N5","ThN5","5^1+2:2s4"]);

MOT("5^1+2:(2^5)",
[
"origin: CAS library,\n",
"maximal subgroup of Ru,\n",
"source: received from S.Mattarei\n",
"test: 1.OR, JAMES, JAMES,n=5,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,5]"
],
[4000,100,1000,80,80,80,80,160,50,20,40,20,20,20,8,8,32,32,40,10,16,16,40,20,
20],
[,[1,2,3,6,6,1,8,1,9,11,3,14,14,2,17,18,8,8,1,9,6,6,8,11,11],,,[1,1,1,4,5,6,7,
8,1,7,8,4,5,6,15,16,17,18,19,19,21,22,23,23,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,-E(4),E(4),-1,1,1,
1,1,1,-E(4),E(4),-1,E(4),-E(4),-1,-1,1,1,-E(4),E(4),-1,-1,-1],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[2,7]],[2,2,2,0,0,-2,-2,2,2,-2,2,0,0,-2,0,0,2,2,0,0,0,0,0,0,0],
[TENSOR,[9,2]],[2,2,2,1+E(4),1-E(4),0,0,-2,2,0,-2,1+E(4),1-E(4),0,0,0,-2*E(4),
2*E(4),0,0,-1-E(4),-1+E(4),0,0,0],
[TENSOR,[11,2]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[8,3,8,4,4,4,0,0,-2,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,2]],
[TENSOR,[15,3]],
[TENSOR,[15,4]],[16,-4,16,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,4,-1,0,0,0,0,0],
[TENSOR,[19,5]],[20,0,-5,0,0,0,-4,4,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-4,1,1],
[TENSOR,[21,2]],[20,0,-5,0,0,0,4,4,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4],
[TENSOR,[23,2]],[40,0,-10,0,0,0,0,-8,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(24,25),( 4, 5)(12,13)(15,16)(17,18)(21,22)]);
ALF("5^1+2:(2^5)","Ru",[1,9,9,5,5,2,5,2,10,27,16,27,27,16,15,15,8,8,3,17,
8,8,6,28,29],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("5^1+2:(2^5)",["RuN5"]);

MOT("5^2:(4xS3)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Suzuki group Suz,\n",
"8th maximal subgroup (and Sylow 5 normalizer) in J2:2,"
],
[600,40,40,24,12,24,24,8,8,50,50,12,10,10,12,12],
[,[1,1,1,1,5,4,4,4,4,10,11,5,10,11,12,12],[1,2,3,4,1,7,6,9,8,10,11,4,13,14,7,
6],,[1,2,3,4,5,6,7,8,9,1,1,12,2,3,15,16]],
[[1,1,-1,-1,1,E(4),-E(4),E(4),-E(4),1,1,-1,1,-1,E(4),-E(4)],
[GALOIS,[1,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[1,-1,1,-1,1,-E(4),E(4),E(4),-E(4),1,1,-1,-1,1,-E(4),E(4)],
[TENSOR,[5,3]],
[TENSOR,[1,5]],
[TENSOR,[1,6]],[2,0,0,-2,-1,-2*E(4),2*E(4),0,0,2,2,1,0,0,E(4),-E(4)],
[TENSOR,[9,3]],
[TENSOR,[9,1]],
[TENSOR,[9,2]],[12,4,0,0,0,0,0,0,0,-3,2,0,-1,0,0,0],
[TENSOR,[13,5]],[12,0,4,0,0,0,0,0,0,2,-3,0,0,-1,0,0],
[TENSOR,[15,1]]],
[( 6, 7)( 8, 9)(15,16),( 2, 3)( 8, 9)(10,11)(13,14)]);
ARC("5^2:(4xS3)","tomfusion",rec(name:="5^2:(4xS3)",map:=[1,2,3,4,5,6,6,7,
7,10,9,13,17,19,21,21],text:=[
"fusion map is unique up to table autom."
]));
ARC("5^2:(4xS3)","CAS",[rec(name:="suzn5",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("5^2:(4xS3)","J2.2",[1,3,2,3,5,19,19,19,19,7,8,10,13,14,24,24],[
"compatible with 5^2:D12 -> J2"
]);
ALF("5^2:(4xS3)","L2(25).2_2",[1,12,13,2,3,4,4,14,14,5,6,7,17,18,8,8],[
"fusion map is unique up to table autom."
]);
ALF("5^2:(4xS3)","Suz",[1,2,3,3,6,10,10,10,10,11,12,17,24,25,30,30],[
"fusion map is unique up to table autom."
]);
ALF("5^2:(4xS3)","G2(4).2",[1,3,2,3,5,27,27,27,27,9,10,12,17,16,34,34],[
"compatible with 5^2:D12 -> G2(4)"
]);
ALF("5^2:(4xS3)","U3(4).4",[1,2,10,10,3,15,16,15,16,5,6,11,7,14,17,18],[
"fusion map is unique up to table autom."
]);
ALN("5^2:(4xS3)",["SuzN5","suzd3","J2.2N5","U3(4).4M4","U3(4).4N5"]);

MOT("5^2:4A4",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Held group He,\n",
"8th maximal subgroup and Sylow 5 normalizer in 2F4(2)',\n",
"maximal subgroup of He"
],
[1200,48,40,12,12,48,48,8,50,12,12,10,12,12,12,12],
[,[1,1,1,5,4,2,2,2,9,4,5,9,10,11,10,11],[1,2,3,1,1,7,6,8,9,2,2,12,6,6,7,7],,[
1,2,3,5,4,6,7,8,1,11,10,3,14,13,16,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1],[
1,1,-1,E(3),E(3)^2,-1,-1,1,1,E(3)^2,E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[2,3]],
[TENSOR,[3,4]],
[TENSOR,[2,5]],[2,-2,0,-E(3)^2,-E(3),-2*E(4),2*E(4),0,2,E(3),E(3)^2,0,
-E(12)^11,-E(12)^7,E(12)^11,E(12)^7],
[TENSOR,[7,2]],
[TENSOR,[7,5]],
[TENSOR,[7,6]],
[TENSOR,[7,4]],
[TENSOR,[7,3]],[3,3,-1,0,0,3,3,-1,3,0,0,-1,0,0,0,0],
[TENSOR,[13,2]],[24,0,-4,0,0,0,0,0,-1,0,0,1,0,0,0,0],
[TENSOR,[15,2]]],
[( 6, 7)(13,15)(14,16),( 4, 5)(10,11)(13,14)(15,16)]);
ARC("5^2:4A4","CAS",[rec(name:="hen5",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("5^2:4A4","tomfusion",rec(name:="5^2:4A4",map:=[1,2,3,4,4,5,5,7,8,9,9,
14,16,16,16,16],text:=[
"fusion map is unique"
]));
ALF("5^2:4A4","He",[1,3,2,5,5,7,7,7,9,11,11,18,20,20,20,20],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("5^2:4A4","2F4(2)'",[1,3,2,4,4,5,5,7,8,9,9,14,15,16,16,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^2:4A4","Fi22N5",[1,2,3,4,4,5,6,11,12,13,13,16,18,18,17,17],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^2:4A4",["HeN5","2f4(2)'n5","max"]);

MOT("7^(1+2):(D8x3)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,7]\n",
"Sylow 7 normalizer in sporadic O'Nan group ON,"
],
[8232,168,84,84,24,24,84,24,24,12,12,12,12,1372,98,98,49,12,12,28,14,14,28,
28],
[,[1,1,1,1,6,5,2,6,5,6,5,6,5,14,15,16,17,9,8,14,16,15,20,20],[1,2,3,4,1,1,7,2,
2,4,4,3,3,14,15,16,17,7,7,20,21,22,23,24],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,
1,1,1,18,19,2,4,3,7,7]],
[[1,1,-1,1,E(3)^2,E(3),-1,E(3)^2,E(3),E(3)^2,E(3),-E(3)^2,-E(3),1,1,1,1,
-E(3)^2,-E(3),1,1,-1,-1,-1],[1,1,1,-1,E(3)^2,E(3),-1,E(3)^2,E(3),-E(3)^2,
-E(3),E(3)^2,E(3),1,1,1,1,-E(3)^2,-E(3),1,-1,1,-1,-1],[1,1,-1,-1,E(3)^2,E(3),
1,E(3)^2,E(3),-E(3)^2,-E(3),-E(3)^2,-E(3),1,1,1,1,E(3)^2,E(3),1,-1,-1,1,1],[1,
1,1,1,E(3)^2,E(3),1,E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),1,1,1,1,E(3)^2,E(3),1,
1,1,1,1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],
[TENSOR,[1,8]],
[TENSOR,[1,7]],
[TENSOR,[1,6]],
[TENSOR,[1,5]],[2,-2,0,0,2*E(3)^2,2*E(3),0,-2*E(3)^2,-2*E(3),0,0,0,0,2,2,2,2,
0,0,-2,0,0,0,0],
[TENSOR,[13,1]],
[TENSOR,[13,5]],[12,0,-6,0,0,0,0,0,0,0,0,0,0,12,5,-2,-2,0,0,0,0,1,0,0],
[TENSOR,[16,1]],[12,0,0,-6,0,0,0,0,0,0,0,0,0,12,-2,5,-2,0,0,0,1,0,0,0],
[TENSOR,[18,2]],[24,0,0,0,0,0,0,0,0,0,0,0,0,24,-4,-4,3,0,0,0,0,0,0,0],[42,-6,
0,0,0,0,-6,0,0,0,0,0,0,-7,0,0,0,0,0,1,0,0,1,1],
[TENSOR,[21,1]],[42,6,0,0,0,0,0,0,0,0,0,0,0,-7,0,0,0,0,0,-1,0,0,
E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,-E(28)^3+E(28)^11
 +E(28)^15-E(28)^19+E(28)^23-E(28)^27],
[TENSOR,[23,1]]],
[(23,24),( 5, 6)( 8, 9)(10,11)(12,13)(18,19),( 3, 4)(10,12)(11,13)(15,16)
(21,22)]);
ARC("7^(1+2):(D8x3)","CAS",[rec(name:="onn7",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("7^(1+2):(D8x3)","ON",[1,2,2,2,3,3,4,7,7,7,7,7,7,8,8,8,9,14,14,15,15,
15,27,28],[
"fusion map is unique up to table autom."
]);
ALF("7^(1+2):(D8x3)","7^(1+2)_+:(3xD16)",[1,7,16,16,5,6,11,8,9,17,18,17,
18,2,3,3,4,12,13,10,19,19,14,15],[
"fusion map is unique up to table autom."
]);
ALF("7^(1+2):(D8x3)","L3(7).2",[1,2,2,17,3,3,18,5,5,19,19,5,5,6,6,7,8,21,
21,11,22,11,25,26],[
"fusion map is unique up to table automorphisms"
]);
ALN("7^(1+2):(D8x3)",["ONN7","L3(7).2M2"]);

MOT("7^(1+2):(S3x3)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,7]\n",
"Sylow 7 normalizer in sporadic Held group He,"
],
[6174,42,63,63,63,18,18,6,6,1029,147,147,98,98,49,14,14,21,21,21,21,21,21],
[,[1,1,4,3,5,7,6,6,7,10,11,12,13,14,15,13,14,19,18,21,20,23,22],[1,2,1,1,1,1,
1,2,2,10,12,11,14,13,15,17,16,11,11,12,12,10,10],,,,[1,2,3,4,5,6,7,8,9,1,1,1,
1,1,1,2,2,3,4,4,3,5,5]],
[[1,-1,E(3),E(3)^2,1,E(3)^2,E(3),-E(3),-E(3)^2,1,1,1,1,1,1,-1,-1,E(3),E(3)^2,
E(3)^2,E(3),1,1],[1,1,E(3),E(3)^2,1,E(3)^2,E(3),E(3),E(3)^2,1,1,1,1,1,1,1,1,
E(3),E(3)^2,E(3)^2,E(3),1,1],[1,-1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,1,1,
1,1],
[TENSOR,[3,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,0,-E(3)^2,-E(3),-1,2*E(3),2*E(3)^2,0,0,2,2,2,2,2,2,0,0,
-E(3)^2,-E(3),-E(3),-E(3)^2,-1,-1],
[TENSOR,[7,1]],
[TENSOR,[7,5]],[6,0,3,3,0,0,0,0,0,6,-3*E(7)-3*E(7)^2-2*E(7)^3-3*E(7)^4
 -2*E(7)^5-2*E(7)^6,-2*E(7)-2*E(7)^2-3*E(7)^3-2*E(7)^4-3*E(7)^5-3*E(7)^6,
2*E(7)^3+2*E(7)^5+2*E(7)^6,2*E(7)+2*E(7)^2+2*E(7)^4,-1,0,0,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,0,0],
[TENSOR,[10,5]],
[GALOIS,[11,5]],
[TENSOR,[12,1]],
[TENSOR,[12,5]],
[TENSOR,[10,1]],[9,-3,0,0,0,0,0,0,0,9,3*E(7)^3+3*E(7)^5+3*E(7)^6,
3*E(7)+3*E(7)^2+3*E(7)^4,2*E(7)+2*E(7)^2+E(7)^3+2*E(7)^4+E(7)^5+E(7)^6,
E(7)+E(7)^2+2*E(7)^3+E(7)^4+2*E(7)^5+2*E(7)^6,2,-E(7)^3-E(7)^5-E(7)^6,
-E(7)-E(7)^2-E(7)^4,0,0,0,0,0,0],
[TENSOR,[16,1]],
[GALOIS,[17,3]],
[TENSOR,[18,1]],[18,0,0,0,0,0,0,0,0,18,-3,-3,4,4,-3,0,0,0,0,0,0,0,0],[42,0,0,
0,6,0,0,0,0,-7,0,0,0,0,0,0,0,0,0,0,0,-1,-1],[42,0,0,0,-3,0,0,0,0,-7,0,0,0,0,0,
0,0,0,0,0,0,E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,
E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19],
[GALOIS,[22,2]]],
[(22,23),(11,12)(13,14)(16,17)(18,21)(19,20)(22,23),( 3, 4)( 6, 7)( 8, 9)
(18,19)(20,21)(22,23),(11,12)(13,14)(16,17)(18,21)(19,20),( 3, 4)( 6, 7)
( 8, 9)(18,19)(20,21)]);
ARC("7^(1+2):(S3x3)","CAS",[rec(name:="hen7",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("7^(1+2):(S3x3)","tomfusion",rec(name:="7^(1+2)+:(S3x3)",map:=[1,2,4,
4,3,5,5,7,7,8,9,9,11,11,10,15,15,23,23,23,23,20,20],text:=[
"fusion map is unique"
]));
ALF("7^(1+2):(S3x3)","He",[1,3,5,5,4,5,5,11,11,14,12,13,15,16,14,23,24,31,
31,30,30,28,29],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("7^(1+2):(S3x3)","7^(1+2):(S3x6)",[1,8,13,14,9,7,6,15,16,2,3,3,5,5,4,
10,10,17,18,18,17,11,12],[
"fusion map is unique up to table automorphisms"
]);
ALN("7^(1+2):(S3x3)",["HeN7"]);

MOT("7^(1+2):(S3x6)",
[
"origin: Dixon's Algorithm\n",
"(group taken from a perm. repr. of He.2),\n",
"Sylow 7 normalizer in He.2 and Fi24',"
],
[12348,2058,147,98,98,36,36,84,126,14,42,42,126,126,12,12,21,21,252,84,126,36,
36,18,18,12,12,42,14,42,42],
[,[1,2,3,4,5,7,6,1,9,5,12,11,14,13,7,6,18,17,1,1,9,6,7,13,14,6,7,2,4,11,12],[1
,2,3,4,5,1,1,8,1,10,2,2,1,1,8,8,3,3,19,20,19,19,19,19,19,20,20,28,29,28,28],,,
,[1,1,1,1,1,6,7,8,9,8,9,9,13,14,15,16,13,14,19,20,21,22,23,24,25,26,27,19,20,
21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1
,-1,1,-1,1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,0,-1,0,-1,-1,-1,-1,0,0,-1,-1,2,0,-1,2,2,-1,-1,0
,0,2,0,-1,-1],
[TENSOR,[5,2]],[1,1,1,1,1,E(3),E(3)^2,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,1,1,1,E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),1,1,1,1],
[TENSOR,[7,7]],
[TENSOR,[2,7]],
[TENSOR,[2,8]],
[TENSOR,[3,7]],
[TENSOR,[3,8]],
[TENSOR,[2,11]],
[TENSOR,[2,12]],
[TENSOR,[5,8]],
[TENSOR,[5,7]],
[TENSOR,[5,10]],
[TENSOR,[5,9]],[12,12,5,-2,-2,0,0,0,0,0,0,0,6,6,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0
,0,0,0],
[TENSOR,[19,7]],
[TENSOR,[19,8]],[18,18,-3,-3,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,
-1,0,0],
[TENSOR,[22,2]],[18,18,-3,4,-3,0,0,-6,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0],
[TENSOR,[24,3]],[42,-7,0,0,0,0,0,0,6,0,-1,-1,0,0,0,0,0,0,6,0,6,0,0,0,0,0,0,-1
,0,-1,-1],
[TENSOR,[26,2]],[42,-7,0,0,0,0,0,0,-3,0,
E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,
E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0,0,0,-6,0,3,0,0,0,0,0,
0,1,0,-E(21)-E(21)^4-E(21)^5-E(21)^16-E(21)^17-E(21)^20,
-E(21)^2-E(21)^8-E(21)^10-E(21)^11-E(21)^13-E(21)^19],
[GALOIS,[28,2]],
[TENSOR,[28,2]],
[TENSOR,[29,2]]],
[(11,12)(30,31),( 4, 5)( 8,20)(10,29)(15,27)(16,26),
( 6, 7)(13,14)(15,16)(17,18)(22,23)(24,25)(26,27)]);
ALF("7^(1+2):(S3x6)","He.2",[1,13,12,13,14,5,5,3,4,20,23,24,5,5,11,11,25,
25,27,27,29,31,31,31,31,31,31,37,37,45,44],[
"fusion map is unique up to table automorphisms"
]);
ALF("7^(1+2):(S3x6)","F3+",[1,25,24,25,25,8,8,3,6,53,71,72,8,8,23,23,70,
70,3,3,14,23,23,23,23,23,23,53,53,105,104],[
"fusion map is unique up to table automorphisms"
]);
ALF("7^(1+2):(S3x6)","7^(1+2)_+:(6xS3).2",[1,2,3,4,4,5,6,11,12,14,15,15,
17,18,22,21,23,24,7,11,13,9,8,20,19,21,22,10,14,16,16],[
"fusion map is unique up to table automorphisms"
]);
ALN("7^(1+2):(S3x6)",["He.2N7","He.2N7C","F3+N7"]);

MOT("7^2:(3x2A4)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,7],\n",
"Sylow 7 normalizer in sporadic Conway group Co1 and in F4(2)"
],
[3528,72,126,126,126,126,72,72,18,18,12,72,72,18,18,18,18,18,18,147,147,12,12,
21,21,21,21],
[,[1,1,4,3,6,5,8,7,10,9,2,7,8,3,4,10,9,6,5,20,21,12,13,25,24,27,26],[1,2,1,1,
1,1,1,1,1,1,11,2,2,2,2,2,2,2,2,20,21,11,11,20,20,21,21],,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,1,1,22,23,3,4,5,6]],
[[1,1,1,1,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),1,E(3),E(3)^2,1,1,E(3)^2,E(3),
E(3),E(3)^2,1,1,E(3)^2,E(3),1,1,E(3),E(3)^2],[1,1,E(3)^2,E(3),1,1,E(3)^2,E(3),
E(3),E(3)^2,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,1,1,1,1,E(3)^2,E(3),E(3)^2,
E(3),1,1],[1,1,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),1,1,1,E(3),E(3)^2,E(3)^2,
E(3),1,1,E(3)^2,E(3),1,1,E(3)^2,E(3),E(3),E(3)^2,E(3)^2,E(3)],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,3]],
[TENSOR,[1,4]],
[TENSOR,[1,5]],
[TENSOR,[1,6]],[2,-2,-1,-1,-E(3),-E(3)^2,2*E(3)^2,2*E(3),-E(3)^2,-E(3),0,
-2*E(3),-2*E(3)^2,1,1,E(3)^2,E(3),E(3),E(3)^2,2,2,0,0,-1,-1,-E(3),-E(3)^2],
[TENSOR,[10,8]],
[TENSOR,[10,9]],
[TENSOR,[10,1]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],
[TENSOR,[10,4]],
[TENSOR,[10,5]],
[TENSOR,[10,6]],[3,3,0,0,0,0,3*E(3)^2,3*E(3),0,0,-1,3*E(3),3*E(3)^2,0,0,0,0,0,
0,3,3,-E(3)^2,-E(3),0,0,0,0],
[TENSOR,[19,1]],
[TENSOR,[19,4]],[24,0,6*E(3),6*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,3,0,0,
-E(3),-E(3)^2,0,0],
[TENSOR,[22,3]],
[TENSOR,[22,2]],[24,0,0,0,6*E(3)^2,6*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,3,-4,0,0,
0,0,-E(3)^2,-E(3)],
[TENSOR,[25,3]],
[TENSOR,[25,1]]],
[( 3, 4)( 5, 6)( 7, 8)( 9,10)(12,13)(14,15)(16,17)(18,19)(22,23)(24,25)
(26,27),( 3, 5)( 4, 6)( 7, 8)(12,13)(14,19)(15,18)(20,21)(22,23)(24,26)
(25,27)]);
ARC("7^2:(3x2A4)","CAS",[rec(name:="c1n7",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("7^2:(3x2A4)","7^2:(3x2S4)",[1,5,11,12,12,11,4,3,13,13,8,6,7,16,15,14,
14,16,15,2,2,10,9,17,18,18,17],[
"fusion map is unique up to table automorphisms"
]);
ALF("7^2:(3x2A4)","(7^2:(3x2A4)xL2(7)).2",[1,3,9,10,10,9,8,7,5,5,4,11,12,
14,13,6,6,14,13,2,2,16,15,17,18,18,17],[
"fusion map determined up to table automorphisms using that the subgroup\n",
"is normal"
]);
ALF("7^2:(3x2A4)","2E6(2)",[1,4,5,5,6,6,7,7,7,7,21,32,32,29,29,32,32,31,
31,34,33,82,81,108,108,107,107],[
"determined by factorization through F4(2)"
]);
ALF("7^2:(3x2A4)","Co1",[1,4,6,6,8,8,8,8,8,8,14,26,26,24,24,26,26,26,26,
27,28,57,57,75,75,76,76],[
"fusion map is unique up to table automorphisms"
]);
ALF("7^2:(3x2A4)","3D4(2).3",[1,3,4,4,22,23,25,24,25,24,8,30,31,10,10,31,
30,28,29,11,12,41,40,20,20,44,45],[
"fusion map is unique up to table aut."
]);
ALF("7^2:(3x2A4)","F4(2)",[1,5,6,6,7,7,8,8,8,8,22,35,35,33,33,35,35,34,34,
36,37,70,69,86,86,87,87],[
"fusion map determined by factorization through 3D4(2).3"
]);
ALN("7^2:(3x2A4)",["2E6(2)N7","3D4(2).3N7","Co1N7","F4(2)N7"]);

MOT("Co1N3",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Conway group Co1,"
],
[157464,1944,1944,1944,216,216,216,216,78732,26244,26244,26244,26244,8748,
8748,8748,8748,4374,2916,2916,2916,2916,2916,2916,2916,2916,1458,1458,1458,
972,972,486,486,486,486,243,162,162,972,972,972,972,972,972,972,972,972,972,
972,972,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,
324,324,324,324,324,324,324,324,324,324,324,324,324,162,162,162,108,108,108,
108,108,108,108,54,54,54,36,36,36,36,36,36,36,36,18,18,18,18,486,486,486,486,
486,486,243,243,243,162,162,162,81,27,54,54,54,54,54,54,54,54,54],
[,[1,1,1,1,1,1,1,1,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,9,9,17,13,9,10,11,13,11,14,10,15,14,19,20,14,15,
10,11,23,24,17,25,21,20,26,25,26,24,23,15,12,24,23,19,17,26,20,25,13,19,16,28,
18,29,12,16,30,31,22,12,22,27,34,35,30,21,30,31,22,21,31,16,32,37,38,33,106,
107,108,109,110,111,112,113,114,115,116,117,118,119,106,107,108,109,110,111,
115,117,116],[1,2,3,4,5,6,7,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,2,4,2,4,3,3,3,3,4,2,4,2,3,4,3,4,3,2,2,4,3,3,2,3,2,4,4,3,4,2,4,2,2,
3,3,4,2,4,3,2,2,4,3,4,2,7,6,3,2,8,5,4,4,2,3,5,7,8,6,7,6,8,5,6,8,5,7,9,9,9,9,9,
9,9,9,9,10,10,10,9,18,39,40,40,39,40,39,44,44,44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,
1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,
-1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,-1,-1,1,-1,1,-1,-1,-1],[1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,
1,-1,-1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,
-1,-1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,
1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[3,4]],
[TENSOR,[2,7]],[2,0,2,0,-2,0,0,-2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
-1,2,2,2,2,-1,2,-1,-1,0,0,0,0,2,2,2,2,0,0,0,0,2,0,2,0,2,0,0,0,2,2,0,2,0,0,0,2,
0,0,0,0,0,2,2,0,0,0,2,0,0,0,2,0,0,0,0,-1,0,-2,-2,0,0,0,-1,1,0,1,0,0,0,-2,-2,0,
1,1,0,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,-1],[2,2,0,0,0,2,0,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,2,-1,2,-1,-1,2,2,0,2,0,0,0,
0,0,0,2,0,2,0,0,0,0,0,2,2,0,0,0,2,0,2,0,0,0,0,2,0,2,2,0,0,0,2,0,0,2,2,0,0,0,2,
0,2,0,-1,2,0,0,0,-1,0,0,0,2,-1,0,2,-1,0,-1,-1,0,0,-1,2,2,-1,2,-1,-1,-1,-1,2,2,
2,-1,-1,-1,0,0,-1,0,-1,0,0,0],
[TENSOR,[10,3]],[2,2,2,2,0,0,0,0,2,2,2,2,2,-1,-1,2,-1,2,-1,-1,2,2,-1,-1,-1,-1,
2,2,-1,2,2,2,2,-1,2,-1,2,2,2,2,-1,2,2,2,2,2,2,-1,2,-1,-1,-1,-1,-1,-1,2,2,-1,
-1,-1,-1,2,-1,-1,-1,-1,-1,-1,-1,2,-1,-1,-1,-1,-1,-1,-1,2,-1,2,2,2,-1,0,0,2,2,
0,0,2,2,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,-1,-1,-1,-1,-1,2,-1,-1,-1,2,-1,2,
-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[12,6]],
[TENSOR,[10,7]],
[TENSOR,[9,2]],
[TENSOR,[12,4]],
[TENSOR,[10,4]],
[TENSOR,[12,2]],
[TENSOR,[9,5]],
[TENSOR,[9,3]],[4,0,4,0,0,0,0,0,4,4,4,4,4,-2,-2,4,-2,4,-2,-2,4,4,-2,-2,-2,-2,
4,4,-2,-2,4,4,4,-2,-2,-2,-2,-2,0,0,0,0,4,4,4,4,0,0,0,0,-2,0,-2,0,-2,0,0,0,-2,
-2,0,4,0,0,0,-2,0,0,0,0,0,-2,-2,0,0,0,-2,0,0,0,4,0,0,0,0,-2,0,0,0,0,0,0,-2,0,
0,0,0,0,0,0,0,0,0,0,0,4,-2,-2,-2,-2,-2,-2,-2,4,1,1,1,-2,1,0,0,0,0,0,0,1,1,1],[
4,4,0,0,0,0,0,0,4,4,4,4,4,-2,-2,4,-2,4,-2,-2,4,4,-2,-2,-2,-2,4,4,-2,4,-2,-2,4,
1,4,1,-2,4,4,0,-2,0,0,0,0,0,0,-2,0,-2,0,0,0,0,0,4,4,0,0,0,-2,0,-2,0,0,0,0,-2,
0,4,-2,0,0,0,-2,0,0,4,-2,0,0,0,-2,0,0,0,-2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,-2,-2,1,-2,1,1,1,-2,-2,-2,-2,-2,1,-2,0,0,1,0,1,0,0,0],
[TENSOR,[21,2]],[4,0,0,0,0,0,0,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-2,
-2,-2,4,-2,-2,-2,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,-2,0,0,0,-2,0,0,1,0,
0,-2,4,4,-2,4,-2,-2,-2,-2,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0],
[TENSOR,[24,3]],
[TENSOR,[22,4]],[6,0,0,-2,0,0,2,-6,6,6,6,6,6,6,6,6,6,6,6,6,6,-3,6,6,6,6,-3,6,
6,0,0,0,-3,0,0,0,0,0,0,-2,0,-2,0,0,0,0,-2,0,-2,0,0,-2,0,-2,0,0,0,-2,0,0,0,0,0,
-2,-2,0,-2,0,-2,0,0,0,0,-2,0,-2,0,0,0,-2,0,-2,0,2,0,0,0,3,0,1,1,0,0,0,2,0,0,
-1,0,0,0,0,0,0,-1,0,-3,-3,0,-3,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0],[6,0,-6,0,
0,-2,2,0,6,6,6,6,6,0,0,6,0,6,0,0,-3,6,0,0,0,0,6,-3,0,0,6,-3,-3,0,0,0,0,0,0,0,
0,0,-6,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,3,0,0,2,-2,0,0,0,0,0,0,0,0,0,-1,0,-2,2,1,0,0,1,0,0,-1,6,0,0,0,0,0,0,0,
-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[28,5]],
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0,0,0,0,0,0,0,0,0],[54,-6,0,0,6,0,-6,0,54,0,0,-27,0,18,18,0,18,0,0,0,0,0,0,0,
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[TENSOR,[100,2]],[54,-6,-6,6,0,0,0,0,-27,-27,0,0,27,-18,9,0,9,0,0,0,0,0,-9,-9,
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[TENSOR,[101,4]],
[TENSOR,[96,4]],
[TENSOR,[97,2]],
[TENSOR,[104,6]],
[TENSOR,[101,2]],
[TENSOR,[104,4]],
[TENSOR,[97,6]],
[TENSOR,[99,2]],
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[TENSOR,[100,6]],
[TENSOR,[102,2]],
[TENSOR,[102,4]],
[TENSOR,[96,6]],
[TENSOR,[99,6]],
[TENSOR,[96,2]],
[TENSOR,[100,4]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0],[108,0,-12,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0],[108,12,0,0,0,0,0,0,108,0,0,-54,0,-18,-18,0,-18,0,0,0,0,
0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,-6,0,-6,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[126,4]],
[TENSOR,[125,2]]],
[( 14, 15, 17)( 19, 23, 25)( 20, 26, 24)( 41, 48, 50)( 51, 55, 60)
( 52, 58, 65)( 53, 66, 59)( 54, 69, 74)( 61, 79, 68)( 63, 75, 71)( 64, 67, 76)
( 72, 77, 73)(115,117,116)(126,127,128)]);
ARC("Co1N3","CAS",[rec(name:="c1n3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("Co1N3","Co1",[1,2,2,2,4,4,4,4,7,7,6,6,5,5,6,6,7,7,7,7,6,6,6,6,7,6,7,
7,7,6,6,8,8,7,7,8,8,8,23,23,21,18,21,23,20,18,20,18,21,20,18,21,21,18,20,
23,22,22,22,23,21,22,23,20,23,22,22,22,22,22,22,22,23,23,20,23,23,18,23,
22,23,23,23,24,24,22,22,24,24,22,23,23,23,24,24,24,24,24,24,24,24,26,26,
26,26,35,36,35,36,37,37,35,37,36,35,36,37,36,36,68,69,68,69,70,70,68,70,
69],[
"computed via intermediate subgroup 3^(3+4):2(S4xS4)"
]);

MOT("Co3N2",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic Conway group Co3,"
],
[1024,1024,512,256,128,128,128,128,128,128,128,64,64,64,64,64,64,32,512,512,
256,256,256,256,256,128,128,128,128,128,128,128,128,128,64,64,64,64,64,64,64,
64,32,16,64,64,64,64,64,64,32,32,32,32,32,32,32,32,32,16,16],
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2,4,3,2,3,4,5,25,25,25,19,25,19,32,32,32,25,33,33,25,19,32,34,21]],
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[TENSOR,[17,9]],
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[TENSOR,[21,5]],[2,2,2,2,-2,-2,0,0,-2,2,-2,0,0,-2,0,0,0,2,2,2,2,2,2,2,2,0,0,0,
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[TENSOR,[23,5]],
[TENSOR,[21,3]],
[TENSOR,[21,1]],
[TENSOR,[23,2]],
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[TENSOR,[29,6]],
[TENSOR,[29,1]],
[TENSOR,[29,2]],[2,2,2,-2,2,0,2,-2,-2,0,0,0,0,0,-2,0,2,0,-2,-2,-2,-2,0,0,2,2,
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[TENSOR,[33,7]],
[TENSOR,[33,1]],
[TENSOR,[33,5]],[4,4,4,-4,-4,0,0,0,4,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,0,0,4,0,0,
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0,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,7]],
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[TENSOR,[43,4]],
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[TENSOR,[43,3]],
[TENSOR,[43,7]],
[TENSOR,[43,5]],
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[TENSOR,[51,1]],
[TENSOR,[51,3]],
[TENSOR,[51,7]],[8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,4,0,-4,
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[TENSOR,[55,4]],
[TENSOR,[55,2]],
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[TENSOR,[59,1]],[16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(30,31)(55,56),(27,29)(55,56),(27,29)(30,31),( 6,11)(15,17)(37,40)(53,59),
( 7, 8)(23,24)(26,28)(45,46)(47,49)(48,50)(51,52)(53,59)]);
ARC("Co3N2","CAS",[rec(name:="co3n2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("Co3N2","Co3",[1,2,2,2,2,2,3,3,3,3,3,3,2,3,3,3,2,3,8,7,8,7,7,8,8,8,7,
7,8,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,18,17,18,18,17,17,19,17,18,19,18,17,19,
19,19,19,19],[
"fusion map is unique up to table autom."
]);
ALF("Co3N2","S6(2)N2",[1,1,3,7,10,17,33,34,16,5,18,40,19,12,37,39,36,42,2,
4,22,22,8,9,6,35,52,32,52,49,49,15,21,11,23,41,47,20,50,48,38,51,14,55,43,
45,44,24,46,25,29,28,26,13,30,30,54,53,27,56,31]);
ALF("Co3N2","2.S6(2)",[1,2,4,4,4,4,6,6,6,6,6,6,4,6,6,6,4,6,5,3,13,14,3,5,
5,5,13,3,14,13,14,5,17,5,17,5,17,5,17,17,5,17,17,17,15,16,15,15,16,16,18,
16,15,18,33,32,18,18,18,18,31],[
"fusion map is unique up to table aut."
]);
ALN("Co3N2",["2.S6(2)N2"]);

MOT("Co3N3",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3],\n",
"Sylow 3 normalizer in sporadic Conway group Co3,\n",
"solvable subgroup of maximal order in Co3"
],
[69984,864,648,288,288,216,34992,2916,1944,1944,972,972,324,162,144,72,48,24,
432,324,216,216,108,108,108,108,108,108,108,36,36,36,36,36,18,48,48,16,16,162,
81,36,36,36,36,36,36,24,12,18,24,24],
[,[1,1,1,1,1,1,7,8,9,10,11,12,13,14,2,2,2,2,7,7,9,10,12,11,12,8,8,12,10,13,13,
10,8,13,14,17,17,17,17,40,41,19,21,24,24,22,21,19,21,40,48,48],[1,2,3,4,5,6,1,
1,1,1,1,1,1,1,15,16,17,18,2,3,2,2,3,2,3,3,6,2,3,3,4,6,5,6,6,36,37,38,39,7,7,
16,15,16,16,15,16,17,18,20,36,37]],
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1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1],[1,1,1,-1,-1,-1,
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1,1,-1,1,1,-1,1,1,-1,1,1,1],
[TENSOR,[1,4]],
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0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[9,4]],
[TENSOR,[9,3]],
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[TENSOR,[13,1]],[4,4,0,0,0,0,4,4,1,-2,1,-2,4,-2,-4,2,0,-2,4,0,1,-2,0,1,0,0,0,
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[TENSOR,[15,6]],
[TENSOR,[15,1]],
[TENSOR,[15,2]],[4,4,2,0,0,-2,4,4,-2,1,-2,1,4,1,-4,0,0,0,4,2,-2,1,-1,-2,-1,2,
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[TENSOR,[19,4]],
[TENSOR,[19,1]],
[TENSOR,[19,2]],[8,-8,0,0,0,0,8,8,-4,2,-4,2,8,2,0,0,0,0,-8,0,4,-2,0,4,0,0,0,
-2,0,0,0,0,0,0,0,0,0,0,0,2,-4,0,0,0,0,0,0,0,0,0,0,0],[8,-8,0,0,0,0,8,8,2,-4,2,
-4,8,-4,0,0,0,0,-8,0,-2,4,0,-2,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,-4,2,0,0,0,0,0,0,
0,0,0,0,0],[8,0,2,8,0,2,8,8,8,8,8,8,-1,-1,0,0,0,0,0,2,0,0,2,0,2,2,2,0,2,-1,-1,
2,0,-1,-1,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,0,0],
[TENSOR,[25,4]],
[TENSOR,[25,2]],
[TENSOR,[25,1]],[16,0,4,0,0,0,16,16,-8,4,-8,4,-2,4,0,0,0,0,0,4,0,0,-2,0,-2,4,
0,0,-2,-2,0,0,0,0,0,0,0,0,0,-5,1,0,0,0,0,0,0,0,0,1,0,0],
[TENSOR,[29,1]],[16,0,0,0,0,-4,16,16,-8,4,-8,4,-2,-5,0,0,0,0,0,0,0,0,0,0,0,0,
-4,0,0,0,0,2,0,2,-1,0,0,0,0,4,1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[31,2]],[18,2,6,0,0,0,-9,0,-6,6,3,-3,0,0,0,2,2,0,-1,-3,2,2,-3,-1,3,0,
0,-1,0,0,0,0,0,0,0,2,2,0,0,0,0,-1,0,-1,-1,0,2,-1,0,0,-1,-1],
[TENSOR,[33,2]],
[TENSOR,[33,1]],
[TENSOR,[33,3]],[32,0,0,0,0,0,32,32,8,-16,8,-16,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0],[36,-4,0,0,0,0,-18,0,
-12,12,6,-6,0,0,0,0,0,0,2,0,-4,-4,0,2,0,0,0,2,0,0,0,0,0,0,0,2*E(8)+2*E(8)^3,
-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[38,1]],[36,4,0,0,0,0,-18,0,-12,12,6,-6,0,0,0,0,-4,0,-2,0,4,4,0,-2,0,
0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0],[72,8,0,0,0,0,-36,0,
-6,-12,3,6,0,0,0,4,0,0,-4,0,2,-4,0,-1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,
1,1,0,-2,0,0,0,0,0],
[TENSOR,[41,2]],[72,8,-12,0,0,0,-36,0,12,6,-6,-3,0,0,0,0,0,0,-4,6,-4,2,-3,2,3,
0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[43,1]],[72,0,-6,0,8,-6,72,-9,0,0,0,0,0,0,0,0,0,0,0,-6,0,0,0,0,0,3,3,
0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[45,4]],
[TENSOR,[45,1]],
[TENSOR,[45,2]],[72,-8,0,0,0,0,-36,0,-6,-12,3,6,0,0,0,0,0,0,4,0,-2,4,0,1,0,0,
0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*E(4),3*E(4),0,0,0,0,0,0,0],
[TENSOR,[49,2]],[72,-8,0,0,0,0,-36,0,12,6,-6,-3,0,0,0,0,0,0,4,0,4,-2,-3,-2,-3,
0,0,1,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[51,1]]],
[(44,45),(36,37)(38,39)(44,45)(51,52),(36,37)(38,39)(51,52)]);
ARC("Co3N3","CAS",[rec(name:="c3n3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("Co3N3","Co3",[1,2,2,3,3,3,4,5,4,5,5,4,5,6,7,7,8,8,11,12,11,13,12,13,
11,13,14,12,13,13,14,14,14,14,15,18,18,19,19,20,21,26,26,28,28,28,26,27,
27,32,41,41],[
"fusion map is unique"
]);
ALF("Co3N3","3^1+4:4s6",[1,4,6,11,11,9,2,3,13,16,14,17,3,18,20,22,24,21,5,
7,28,30,34,29,33,8,10,31,32,8,12,36,12,10,37,43,43,38,39,19,15,23,47,50,
51,48,49,25,52,35,44,44],[
"fusion map is unique up to table automorphisms"
]);
ALN("Co3N3",["3^(1+4):4.3^2:D8"]);

MOT("Fi22N3",
[
"origin: Ostermann\n",
"Sylow 3 normalizer in sporadic Fischer group Fi22,\n",
"3rd power map computed from the group"
],
[78732,108,108,108,39366,13122,4374,4374,4374,4374,4374,4374,4374,1458,1458,
1458,1458,1458,1458,1458,1458,1458,1458,1458,1458,1458,1458,1458,1458,1458,
1458,1458,1458,1458,729,729,729,729,729,729,729,729,729,729,486,486,486,486,
486,486,486,486,486,243,81,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,
54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,81,81,81,81,
81,81,27,27,27],
[,[1,1,1,1,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,21,18,11,16,33,14,25,12,9,17,7,15,22,32,5,46,53,27,45,19,52,28,23,20,29,6,
31,24,34,10,30,47,49,48,51,50,13,8,26,95,96,97,98,99,100,101,102,103],[1,2,3,
4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,3,4,4,4,4,3,3,3,4,4,4,2,2,2,2,2,3,2,2,3,4,3,3,
3,3,3,3,3,2,2,2,2,2,4,4,2,6,5,6,5,5,6,8,13,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1],[1,1,-1,-1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1],
[TENSOR,[2,3]],[2,-2,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,2,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-2,-2,-2,1,-2,0,1,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,1,2,-1,-1,-1,-1,
-1,2,-1,-1],
[TENSOR,[5,2]],[2,-2,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,2,
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-1,-1,-1,2],
[TENSOR,[7,2]],[2,-2,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,2,
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-1,2,-1,2,-1],
[TENSOR,[9,2]],[2,0,0,-2,2,2,2,2,2,2,2,2,2,-1,-1,2,2,-1,2,-1,-1,-1,2,2,-1,2,2,
2,2,2,2,-1,-1,2,-1,-1,-1,-1,2,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,-1,1,1,-2,0,
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2,-1,2,2,-1,-1,-1],
[TENSOR,[11,2]],[2,2,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
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2,2,-1,-1,-1,-1],
[TENSOR,[13,2]],[4,0,0,0,4,4,4,4,4,4,4,4,4,-2,-2,4,4,-2,4,-2,-2,-2,4,4,-2,-2,
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4,1,-2,1,-2,-2,-2,1,1],[4,0,0,0,4,4,4,4,4,4,4,4,4,-2,-2,4,4,-2,4,-2,-2,-2,4,4,
-2,-2,-2,-2,4,4,4,-2,-2,4,-2,-2,-2,-2,4,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,4,4,4,
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0,0,0,0,-2,1,4,1,-2,-2,1,1,-2],[4,0,0,0,4,4,4,4,4,4,4,4,4,-2,-2,4,4,-2,4,-2,
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0,0,0,0,0,0,0,0,0,-2,1,-2,1,-2,4,1,-2,1],[4,0,0,0,4,4,4,4,4,4,4,4,4,-2,-2,4,4,
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0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,4,-2,1,1,1],[6,0,0,-2,6,6,6,-3,6,6,6,-3,
-3,-3,3,0,0,3,0,0,3,0,0,0,0,6,6,6,0,0,0,-3,-3,0,-3,0,0,3,-3,3,0,3,-3,-3,0,0,0,
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0,0,0,0,0,0,0,0,1,1,0,0,3,0,-3,0,0,0,0,0],[6,0,0,-2,6,6,6,-3,6,6,6,-3,-3,3,0,
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0,0,0,0,0,1,1,0,0,0,0,3,0,0,0,0,0],[6,0,0,-2,6,6,6,-3,6,6,6,-3,-3,0,-3,0,0,-3,
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1,1,0,0,-3,0,0,0,0,0,0,0],[6,0,-2,0,6,6,-3,6,-3,-3,6,6,6,0,0,6,-3,0,-3,0,0,0,
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[TENSOR,[25,3]],
[TENSOR,[19,2]],
[TENSOR,[20,2]],
[TENSOR,[21,2]],
[TENSOR,[22,3]],
[TENSOR,[23,3]],
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0,0,0,0,0,0,0],[54,-2,0,0,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9,0,9,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,6,-3,-3,6,6,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,-2,1,-2,1,0,1,1,0,0,0,0,0,0,0,0,0,1,-2,1,1,-2,0,0,1,0,0,0,0,0,0,0,
0,0],[54,-2,0,0,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-3,6,6,-3,-3,-3,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,-2,1,1,1,0,-2,1,0,0,0,0,0,0,0,0,0,-2,1,1,1,1,0,0,-2,0,0,0,0,0,0,0,0,0],[54,
-2,0,0,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-3,6,-3,6,-3,-3,6,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-2,1,1,
1,0,1,-2,0,0,0,0,0,0,0,0,0,1,1,-2,-2,1,0,0,1,0,0,0,0,0,0,0,0,0],
[TENSOR,[86,2]],
[TENSOR,[87,2]],
[TENSOR,[88,2]],
[TENSOR,[89,2]],
[TENSOR,[90,2]],
[TENSOR,[91,2]],
[TENSOR,[92,2]],
[TENSOR,[93,2]],
[TENSOR,[94,2]]],
[(45,46,53)(47,49,48)(50,52,51)(71,72,74)(76,90,91)(87,88,89),(45,53,46)
(47,48,49)(50,51,52)(71,74,72)(76,91,90)(87,89,88),(26,28,27)(47,48,49)
(50,52,51)(73,94,77)(76,90,91)(87,89,88),(26,28,27)(45,46,53)(50,51,52)
(71,72,74)(73,94,77)(76,91,90),(14,33,32)(15,21,18)(16,24,30)(17,29,34)
(19,31,23)(20,25,22)(35,44,43)(36,37,41)(38,40,42)(56,57,67)(59,83,86)
(60,69,61)(62,68,79)(65,80,84)(75,82,78),( 12, 13)( 15, 21)( 16, 17)( 22, 25)
( 23, 31)( 24, 34)( 26, 28, 27)( 29, 30)( 32, 33)( 35, 43)( 36, 37)( 38, 42)
( 46, 53)( 47, 50, 49, 51, 48, 52)( 56, 67)( 59, 65)( 60, 69)( 62, 68)
( 63, 92)( 71, 72)( 73, 94, 77)( 76, 87, 91, 88, 90, 89)( 78, 82)( 80, 86)
( 83, 84)( 97,100)(102,103),(  8, 12)( 15, 18)( 16, 19)( 20, 22)( 23, 24)
( 26, 27, 28)( 29, 34)( 30, 31)( 32, 33)( 35, 43)( 37, 41)( 40, 42)
( 45, 50, 46, 51, 53, 52)( 48, 49)( 57, 67)( 59, 75)( 60, 69)( 63, 93)
( 68, 79)( 71, 90, 72, 76, 74, 91)( 73, 77, 94)( 78, 83)( 80, 84)( 82, 86)
( 88, 89)( 95, 97)(101,103)]);
ARC("Fi22N3","CAS",[rec(name:="f22n3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("Fi22N3","Fi22",[1,4,4,4,6,6,5,6,7,6,7,6,8,8,7,8,8,7,6,8,7,6,7,6,6,7,
5,6,8,7,8,5,8,7,8,8,8,8,8,8,8,6,7,7,6,7,7,8,8,8,6,7,8,8,8,24,24,22,25,25,
25,21,21,24,25,20,22,21,20,21,22,25,20,21,21,22,21,22,25,25,21,25,21,24,
21,22,24,25,25,21,25,25,21,24,32,32,32,31,32,32,32,33,32],[
"fusion map is unique up to table automorphisms\n,",
"compatible with 2xFi22N3 -> 2.Fi22 and 3.Fi22N3 -> 3.Fi22"
]);
ALF("Fi22N3","O7(3)",[1,4,4,4,5,5,6,5,7,5,7,8,9,6,10,10,10,7,7,5,10,8,9,
11,9,5,7,6,9,8,8,11,11,11,10,11,11,8,11,11,11,9,10,11,7,9,10,9,11,8,10,11,
8,11,11,31,26,21,31,32,25,29,28,26,30,25,30,28,32,23,29,28,26,21,21,32,25,
29,23,29,23,28,32,32,23,28,30,32,29,31,28,29,23,23,37,37,37,36,37,37,37,
39,38]);
ALN("Fi22N3",["f22n3","O7(3)N3"]);

MOT("Fi22N5",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Fischer group Fi22,"
],
[2400,96,80,12,96,96,80,80,16,16,16,100,12,8,8,20,12,12,20,20],
[,[1,1,1,4,2,2,3,3,3,3,2,12,4,6,5,12,13,13,16,16],[1,2,3,1,6,5,8,7,10,9,11,12,
2,15,14,16,6,5,20,19],,[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,3,17,18,7,8]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,
-1,1,1,1,-1,-1],[1,1,-1,1,-1,-1,E(4),-E(4),E(4),-E(4),1,1,1,E(4),-E(4),-1,-1,
-1,E(4),-E(4)],
[TENSOR,[2,3]],[2,-2,0,-1,-2*E(4),2*E(4),1-E(4),1+E(4),-1+E(4),-1-E(4),0,2,1,
0,0,0,E(4),-E(4),1-E(4),1+E(4)],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[2,2,-2,-1,-2,-2,0,0,0,0,2,2,-1,0,0,-2,1,1,0,0],
[TENSOR,[9,3]],[3,3,1,0,-3,-3,-E(4),E(4),-E(4),E(4),-1,3,0,E(4),-E(4),1,0,0,
-E(4),E(4)],
[TENSOR,[11,2]],
[TENSOR,[11,4]],
[TENSOR,[11,3]],[4,-4,0,1,-4*E(4),4*E(4),0,0,0,0,0,4,-1,0,0,0,-E(4),E(4),0,0],
[TENSOR,[15,3]],[24,0,-4,0,0,0,4*E(4),-4*E(4),0,0,0,-1,0,0,0,1,0,0,-E(4),
E(4)],
[TENSOR,[17,2]],
[TENSOR,[17,4]],
[TENSOR,[17,3]]],
[( 5, 6)( 7, 8)( 9,10)(14,15)(17,18)(19,20)]);
ARC("Fi22N5","CAS",[rec(name:="f22n5",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("Fi22N5","Fi22",[1,4,3,8,12,12,10,10,13,13,12,14,25,30,30,35,48,48,59,
59],[
"fusion map is unique"
]);
ALF("Fi22N5","He.2",[1,3,2,5,7,7,28,28,28,28,7,9,11,34,34,16,18,18,40,40],[
"fusion map is unique"
]);
ALF("Fi22N5","O8+(2).3.2",[1,4,3,29,11,11,44,44,48,48,11,12,32,57,57,23,
37,37,66,66],[
"fusion map is unique"
]);
ALF("Fi22N5","2F4(2)'.2",[1,3,2,4,5,5,18,19,21,21,7,8,9,23,23,13,14,14,28,
29],[
"fusion map is unique up to table automorphisms"
]);
ALF("Fi22N5","2xFi22N5",[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,
37,39],[
"fusion map is unique up to table aut."
]);
ALF("Fi22N5","F4(2)",[1,5,4,8,20,20,14,14,21,21,20,24,35,47,47,53,68,68,
85,85],[
"fusion map determined by factorization through 2F4(2)'.2"
]);
ALN("Fi22N5",["f22n5","2F4(2)'.2N5","F4(2)N5","He.2N5","O8+(2).3.2N5"]);

MOT("HS.2N5",
[
"origin: Dixon's algorithm,\n",
"maximal subgroup of HS.2,\n",
"Sylow 5 normalizer in HS.2,\n",
"table is sorted w.r. to normal series 5.5^2.8.2.2,\n",
"tests: 1.o.r., pow[2,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["5^1+2:(2^5)"],(2,3)(4,17,8,5,19,15,10,12,18,7,11,6,13,
20,16,9)(21,24)(22,25,23),(2,7)(3,4,9)(6,10,8)(12,14,13)(15,17,18)]);
ARC("HS.2N5","projectives",["2.HS.2N5",[[2,2,2,2,-2,-2,0,0,-1-E(4),-1+E(4),0,
0,-2*E(4),-2*E(4),0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[8,8,3,-2,0,0,0,0,0,0,0,0,-4*E(4),E(4),0,0,0,E(40)^13-E(40)^21
 -E(40)^29+E(40)^37,0,-E(40)^7-E(40)^23+E(40)^31+E(40)^39,0,0,0,0,0],[16,16,
-4,1,0,0,0,0,0,0,0,0,0,0,0,-E(5)+E(5)^2+E(5)^3-E(5)^4,0,0,0,0,0,0,0,0,0],[20,
-5,0,0,4,-1,0,0,0,0,0,-E(5)+E(5)^2+E(5)^3-E(5)^4,0,0,0,0,0,0,0,0,
-E(5)+E(5)^2-E(5)^3+E(5)^4,0,E(5)+E(5)^2-E(5)^3-E(5)^4,0,0],
[GALOIS,[5,3]],[40,-10,0,0,-8,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("HS.2N5","HS.2",[1,8,9,10,2,16,7,7,15,15,5,21,3,17,23,33,26,36,26,36,
37,24,38,26,26],[
"fusion map is unique up to table automorphisms"
]);

MOT("HSN2",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic Higman Sims group HS"
],
[512,512,256,128,64,64,32,32,32,32,256,256,128,128,128,64,64,64,64,64,64,64,
32,32,32,32,16,16,16,16,16,16,16,16,16],
[,[1,1,1,1,1,1,1,1,1,1,2,2,3,2,3,4,4,4,3,4,2,2,2,2,3,3,6,6,13,13,21,21,14,14,
12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,
1,1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,
-1],[1,1,1,1,1,1,-1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,
-1,-1,1],
[TENSOR,[2,3]],[1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,1,
-1,-1,-1,-1,-1,1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,-2,2,-2,0,0,0,0,-2,-2,-2,2,-2,0,0,0,2,0,-2,2,0,0,0,0,0,
0,2*E(4),-2*E(4),0,0,0,0,0],
[TENSOR,[9,5]],[2,2,2,-2,2,2,0,0,0,0,-2,-2,2,2,2,0,0,0,-2,0,-2,-2,0,0,0,0,2,
-2,0,0,0,0,0,0,0],
[TENSOR,[11,3]],[2,2,2,-2,-2,2,0,2,-2,0,-2,-2,-2,2,-2,0,0,0,2,0,2,-2,0,0,2,-2,
0,0,0,0,0,0,0,0,0],
[TENSOR,[13,2]],[2,2,2,-2,-2,-2,0,0,0,0,-2,-2,2,2,2,0,0,0,-2,0,2,2,0,0,0,0,0,
0,0,0,-2,2,0,0,0],
[TENSOR,[15,2]],[2,2,2,2,2,-2,2,0,0,0,2,2,-2,2,-2,0,0,0,-2,0,2,-2,2,0,0,0,0,0,
0,0,0,0,-2,0,0],
[TENSOR,[17,3]],[2,2,2,2,-2,-2,0,0,0,0,2,2,2,2,2,-2,-2,-2,2,-2,-2,-2,0,0,0,0,
0,0,0,0,0,0,0,0,2],
[TENSOR,[19,2]],[2,2,2,2,-2,2,0,0,0,2,2,2,-2,2,-2,0,0,0,-2,0,-2,2,0,2,0,0,0,0,
0,0,0,0,0,-2,0],
[TENSOR,[21,2]],[4,4,-4,0,0,0,-2,0,0,2,-4,4,0,0,0,-2,2,2,0,-2,0,0,2,-2,0,0,0,
0,0,0,0,0,0,0,0],
[TENSOR,[23,2]],
[TENSOR,[23,3]],
[TENSOR,[23,4]],[4,4,4,4,0,0,0,-2,2,0,-4,-4,0,-4,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,
0,0,0,0,0,0,0],
[TENSOR,[27,2]],[4,4,4,-4,0,0,0,-2,-2,0,4,4,0,-4,0,0,0,0,0,0,0,0,0,0,2,2,0,0,
0,0,0,0,0,0,0],
[TENSOR,[29,2]],[8,8,-8,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[8,-8,0,0,0,0,0,0,0,0,0,0,4,0,-4,-4,0,0,0,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[32,2]],[8,-8,0,0,0,0,0,0,0,0,0,0,-4,0,4,0,4*E(4),-4*E(4),0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[34,2]]],
[(29,30),(17,18),(17,18)(29,30),(16,20),( 8, 9)(25,26),(31,32),(27,28)]);
ARC("HSN2","CAS",[rec(name:="hsn2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("HSN2","HS",[1,2,2,2,3,2,3,2,3,2,5,6,6,6,5,5,6,6,6,6,7,6,7,6,7,6,6,7,
14,14,15,16,14,14,14],[
"fusion map is unique up to table automorphisms"
]);

MOT("J2N2",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 2 normalizer in sporadic Janko group J2"
],
[384,384,192,48,16,24,24,48,32,16,24,24,12,12,12,12,8,12,12],
[,[1,1,1,1,1,7,6,2,2,3,6,7,7,6,7,6,9,11,12],[1,2,3,4,5,1,1,8,9,10,2,2,3,3,4,4,
17,8,8]],
[[1,1,1,1,1,E(3)^2,E(3),1,1,1,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),1,E(3)^2,
E(3)],[1,1,1,-1,1,E(3)^2,E(3),-1,1,1,E(3),E(3)^2,E(3)^2,E(3),-E(3)^2,-E(3),-1,
-E(3)^2,-E(3)],[1,1,1,-1,1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1],
[TENSOR,[3,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[3,3,3,-3,-1,0,0,-3,3,-1,0,0,0,0,0,0,1,0,0],
[TENSOR,[7,2]],[4,4,-4,2,0,E(3)^2,E(3),-2,0,0,E(3),E(3)^2,-E(3)^2,-E(3),
-E(3)^2,-E(3),0,E(3)^2,E(3)],
[TENSOR,[9,3]],
[TENSOR,[9,5]],
[TENSOR,[9,6]],
[TENSOR,[9,2]],
[TENSOR,[9,1]],[6,6,6,0,-2,0,0,0,-2,2,0,0,0,0,0,0,0,0,0],[6,6,6,0,2,0,0,0,-2,
-2,0,0,0,0,0,0,0,0,0],[8,-8,0,0,0,2*E(3)^2,2*E(3),0,0,0,-2*E(3),-2*E(3)^2,0,0,
0,0,0,0,0],
[TENSOR,[17,1]],
[TENSOR,[17,5]]],
[( 6, 7)(11,12)(13,14)(15,16)(18,19)]);
ARC("J2N2","CAS",[rec(name:="j2n2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("J2N2","J2",[1,2,2,2,3,4,4,6,6,6,11,11,11,11,11,11,14,19,19],[
"fusion map is unique"
]);
ALF("J2N2","2^(2+4).(S3x2)",[1,2,3,14,5,7,7,16,4,6,8,8,9,9,17,17,22,23,23],[
"fusion map is unique"
]);

MOT("J3N2",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 2 normalizer in sporadic Janko group J3"
],
0,
0,
0,
0,
["ConstructPermuted",["J2N2"],(15,16)(18,19),(1,5,2,6)(3,4)(7,8)(9,10)(11,13,
12,14)(15,16)]);
ARC("J3N2","CAS",[rec(name:="j3n2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("J3N2","J3",[1,2,2,2,2,3,3,5,5,5,8,8,8,8,8,8,9,15,15],[
"fusion map is unique"
]);
ALF("J3N2","2^(2+4).(S3x2)",[1,2,3,14,5,7,7,16,4,6,8,8,9,9,17,17,22,23,23],[
"fusion map is unique"
]);

MOT("LyN2",
[
"origin: constructed from the Sylow 2 subgroup of A11 by K.Lux,\n",
"(Note: The table in Ostermann's paper is fishy!)\n",
"tests: 1.o.r.\n",
"Sylow 2 normalizer in sporadic Lyons group Ly,\n",
"Sylow 2 normalizer in McL.2,\n",
"Sylow 2 subgroup of 2.A11,"
],
[256,256,128,64,32,32,32,32,32,32,16,16,32,32,32,16,16,16,8,8,16,16],
[,[1,1,1,2,1,2,1,2,1,2,1,1,3,4,4,3,4,4,5,6,13,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,1,1,1,
1,-1,1,1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1],
[TENSOR,[2,3]],[1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1],
[TENSOR,[3,5]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],[2,2,2,2,2,-2,-2,-2,0,0,0,0,-2,0,0,0,2,0,0,0,0,0],
[TENSOR,[9,5]],[2,2,2,2,-2,2,0,0,-2,-2,0,0,-2,0,0,0,0,2,0,0,0,0],
[TENSOR,[11,3]],[2,2,2,2,-2,-2,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0,0],
[TENSOR,[13,3]],[4,4,4,-4,0,0,0,0,0,0,2,0,0,0,0,-2,0,0,0,0,0,0],
[TENSOR,[15,2]],[4,4,-4,0,0,0,-2,2,2,-2,0,0,0,-2,2,0,0,0,0,0,0,0],
[TENSOR,[17,3]],
[TENSOR,[17,6]],
[TENSOR,[17,5]],[8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2],
[TENSOR,[21,2]]],
[(21,22)]);
ALF("LyN2","A11Syl2",[1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,20]);
ALF("LyN2","Ly",[1,2,2,5,2,5,2,5,2,5,2,2,5,12,13,5,12,13,5,13,12,13],[
"fusion map is unique up to table automorphism (21,22) of LyN2"
]);
ALF("LyN2","McL.2",[1,2,2,5,2,5,2,5,20,21,2,20,5,23,24,5,11,24,5,24,23,24],[
"fusion map is unique up to table automorphisms"
]);
ALF("LyN2","Isoclinic(2.A8.2)",[1,2,3,4,3,4,3,4,20,19,3,20,9,21,22,9,10,
22,9,22,26,27],[
"fusion map is unique up to table aut."
]);
ALF("LyN2","2.A11",[1,2,4,3,4,3,4,3,4,3,4,4,12,11,13,12,11,13,12,13,27,26],[
"fusion map is unique up to table automorphism (21,22) of LyN2"
]);
ALN("LyN2",["(2.A11)Syl2","McL.2N2"]);

MOT("LyN3",
[
"origin: Ostermann,\n",
"Sylow 3 normalizer in sporadic Lyons group Ly,\n",
"tests: 1.o.r., pow[2,3]"
],
[69984,864,648,288,288,216,17496,17496,3888,972,972,972,324,162,144,72,48,24,
432,324,216,216,108,108,108,108,108,108,108,36,36,36,36,36,18,48,48,16,16,54,
36,36,36,36,36,36,24,12,18,24,24],
[,[1,1,1,1,1,1,7,8,9,10,11,12,13,14,2,2,2,2,9,8,7,8,11,11,10,8,12,11,9,13,12,
13,12,13,14,17,17,17,17,40,19,25,25,21,22,21,19,21,40,47,47],[1,2,3,4,5,6,1,1,
1,1,1,1,1,1,15,16,17,18,2,3,2,2,3,2,2,6,3,3,3,5,4,6,6,3,6,36,37,38,39,8,16,16,
16,15,15,16,17,18,20,36,37]],
[[1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-1,1,1,-1,1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,
1,-1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,-1,-1],[1,1,-1,-1,-1,1,1,1,1,1,1,1,1,
1,-1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,
-1,-1,1,1,-1,1,1],[1,1,-1,1,1,-1,1,1,1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,
-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,1,1],[1,1,-1,1,1,
-1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,-2,0,0,0,2,2,-1,-1,-1,2,2,2,0,2,2,0,-1,-2,2,2,1,-1,-1,0,
-2,1,1,0,0,0,0,-2,0,-2,-2,0,0,-1,-1,-1,-1,0,0,2,-1,0,1,1,1],
[TENSOR,[9,6]],
[TENSOR,[9,2]],
[TENSOR,[9,1]],[2,-2,0,2,-2,0,2,2,2,2,2,2,2,2,0,0,0,0,-2,0,-2,-2,0,-2,-2,0,0,
0,0,-2,2,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,2,0,0,0,0,
0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[13,4]],
[TENSOR,[13,2]],
[TENSOR,[13,1]],[2,2,0,-2,-2,0,2,2,2,2,2,2,2,2,2,0,-2,0,2,0,2,2,0,2,2,0,0,0,0,
-2,-2,0,0,0,0,0,0,0,0,2,0,0,0,2,2,0,-2,0,0,0,0],
[TENSOR,[17,1]],[4,-4,0,0,0,0,4,4,-2,-2,-2,4,4,4,0,0,0,0,2,0,-4,-4,0,2,2,0,0,
0,0,0,0,0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,-2,0,0,0,0,0,0,0,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[19,1]],[4,4,0,0,0,0,4,4,-2,-2,-2,4,4,4,0,0,-4,0,-2,0,4,4,0,-2,-2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,2,0,0,0,0],[8,0,-2,0,8,-2,8,8,8,8,8,8,
-1,-1,0,0,0,0,0,-2,0,0,-2,0,0,-2,-2,-2,-2,-1,0,1,-2,1,1,0,0,0,0,-1,0,0,0,0,0,
0,0,0,1,0,0],
[TENSOR,[22,5]],
[TENSOR,[22,3]],
[TENSOR,[22,1]],[16,0,4,0,0,0,16,16,-8,-8,-8,16,-2,-2,0,0,0,0,0,4,0,0,-2,0,0,
0,4,-2,-2,0,0,0,0,-2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],
[TENSOR,[26,1]],[24,0,-6,8,0,-2,24,24,0,0,0,-3,6,-3,0,0,0,0,0,-6,0,0,0,0,0,-2,
3,0,0,0,-1,-2,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[28,3]],
[TENSOR,[28,1]],
[TENSOR,[28,5]],[36,4,-6,0,0,6,-18,9,12,-6,3,0,0,0,-4,0,0,0,4,3,-2,1,-3,1,-2,
-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0],
[TENSOR,[32,5]],
[TENSOR,[32,1]],
[TENSOR,[32,3]],[36,4,0,0,0,0,9,-18,-12,-3,6,0,0,0,-4,-2,0,2,4,0,1,-2,0,-2,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,1,-1,2,1,0,-1,0,0,0],
[TENSOR,[36,2]],
[TENSOR,[36,1]],
[TENSOR,[36,3]],[48,0,0,0,0,-4,48,48,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,-4,0,
0,0,0,0,2,2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[40,3]],[72,8,12,0,0,0,-36,18,-12,6,-3,0,0,0,0,0,0,0,-4,-6,-4,2,-3,-1,
2,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[72,-8,0,0,0,0,-36,18,
-12,6,-3,0,0,0,0,0,0,0,4,0,4,-2,-3,1,-2,0,0,-3,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[TENSOR,[42,1]],
[TENSOR,[43,1]],[72,-8,0,0,0,0,18,-36,-24,-6,12,0,0,0,0,0,0,0,-8,0,-2,4,0,4,
-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[72,-8,0,0,0,0,-36,18,
24,-12,6,0,0,0,0,0,0,0,-8,0,4,-2,0,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[72,-8,0,0,0,0,18,-36,12,3,-6,0,0,0,0,0,0,0,4,0,-2,4,0,-2,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*E(4),-3*E(4),0,0,0,0,0,0,0,0],
[TENSOR,[48,2]],[72,8,0,0,0,0,18,-36,12,3,-6,0,0,0,0,-4,0,0,-4,0,2,-4,0,2,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,0,0,2,0,0,0,0,0],
[TENSOR,[50,2]]],
[(42,43),(36,37)(38,39)(42,43)(50,51),(36,37)(38,39)(50,51)]);
ARC("LyN3","CAS",[rec(name:="lyn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("LyN3","Ly",[1,2,2,2,2,2,3,4,3,4,4,4,4,4,5,5,5,5,8,10,8,9,10,10,9,10,
9,9,8,10,10,9,10,10,10,12,12,13,13,14,19,20,20,19,20,19,19,19,25,31,31],[
"fusion map is unique"
]);
ALF("LyN3","Suz.2",[1,2,2,39,39,39,4,5,4,5,5,5,5,6,40,40,9,9,13,14,13,15,
14,14,15,43,15,15,13,43,43,43,43,15,45,50,50,20,20,21,54,55,55,54,55,54,
27,27,34,64,64],[
"fusion map is unique"
]);

MOT("LyN5",
[
"origin: Ostermann,\n",
"Sylow 5 normalizer in sporadic Lyons group Ly,\n",
"tests: 1.o.r., pow[2,5]"
],
[250000,400,400,400,80,80,80,80,80,80,80,80,80,80,80,80,62500,12500,2500,2500,
2500,1250,1250,1250,1250,625,625,625,625,625,500,250,250,100,100,100,100,100,
100,50,50,50,50,50,50,20,20,20,20,20,20,20,20,20,20,20,20,25],
[,[1,1,1,1,2,2,3,3,4,4,4,4,3,3,2,2,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,19,31,20,18,17,21,24,25,32,22,33,23,34,34,35,35,36,36,38,38,39,39,37,
37,58],,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,2,4,3,2,4,3,2,2,4,3,4,3,5,6,11,12,7,8,9,10,14,13,15,16,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,-E(4),E(4),1,1,E(4),-E(4),
-E(4),E(4),-1,-1,-E(4),E(4),1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,
-1,-1,-1,1,-1,1,-E(4),E(4),-E(4),E(4),1,1,E(4),-E(4),-1,-1,-E(4),E(4),1],[1,1,
-1,-1,1,1,E(4),-E(4),-E(4),E(4),-E(4),E(4),E(4),-E(4),-1,-1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-E(4),E(4),E(4),-E(4),
-E(4),E(4),-E(4),E(4),-1,-1,1],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[3,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[2,8]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],
[TENSOR,[2,12]],
[TENSOR,[2,13]],
[TENSOR,[2,15]],[4,0,0,4,0,0,0,0,0,0,-4,-4,0,0,0,0,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,-1,-1,-1,0,-1,0,0,4,0,0,0,-1,0,-1,0,0,0,1,1,0,0,0,0,0,0,0,0,-1],
[TENSOR,[17,2]],
[TENSOR,[17,4]],
[TENSOR,[17,7]],[4,0,4,0,0,0,-4,-4,0,0,0,0,0,0,0,0,4,4,4,-1,4,-1,-1,4,4,-1,-1,
-1,-1,-1,4,4,4,0,0,-1,0,0,4,0,0,0,-1,0,-1,0,0,0,0,1,1,0,0,0,0,0,0,-1],
[TENSOR,[21,6]],
[TENSOR,[21,3]],
[TENSOR,[21,10]],[16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,16,16,-4,16,-4,-4,16,16,
-4,-4,-4,-4,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[
20,-4,0,0,-4*E(4),4*E(4),0,0,0,0,0,0,0,0,0,0,20,20,-5,0,20,0,0,-5,-5,0,0,0,0,
0,0,0,0,1,0,0,-4,0,0,1,1,0,0,0,0,E(4),-E(4),0,0,0,0,0,0,0,0,0,0,0],[20,0,4,0,
0,0,0,0,0,0,0,0,-4,-4,0,0,20,20,0,0,-5,-5,5,0,0,0,-5,5,5,-5,0,0,0,0,0,4,0,0,
-1,0,0,0,-1,0,-1,0,0,0,0,0,0,0,0,1,1,0,0,0],
[TENSOR,[26,2]],
[TENSOR,[26,4]],
[TENSOR,[27,5]],[20,-4,0,0,0,0,0,0,0,0,0,0,0,0,-4*E(4),4*E(4),20,-5,0,0,0,10,
0,-5,5,0,-5,5,-5,0,0,0,0,-4,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(4),
-E(4),0],
[TENSOR,[27,3]],
[TENSOR,[26,7]],
[TENSOR,[31,2]],
[TENSOR,[31,5]],
[TENSOR,[31,3]],
[TENSOR,[27,2]],[40,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,40,40,0,10,-10,0,-5,0,0,10,
0,-5,-5,0,0,0,0,0,0,-2,0,0,-2,0,0,0,-2,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0],[40,-8,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,40,-10,-10,20,0,0,10,5,0,-5,-5,-5,0,5,0,0,0,2,0,0,
2,0,0,-3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[40,0,8,0,0,0,0,0,0,0,0,0,0,0,0,
0,40,40,0,-10,-10,5,0,0,0,-10,5,0,0,5,0,0,0,0,0,-2,0,0,-2,0,0,0,3,0,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0],[40,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,40,-10,10,0,0,10,10,0,
-5,0,5,-5,0,-10,0,0,0,-2,0,0,-2,0,0,-2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[40,3]],
[TENSOR,[38,3]],
[TENSOR,[39,2]],
[TENSOR,[41,2]],[80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,80,-20,-20,0,0,10,-20,10,0,
0,0,0,10,-5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,80,-20,-20,-20,0,-10,10,10,0,5,5,5,-10,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,80,-20,20,-20,0,0,0,0,-10,5,-10,-5,5,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,80,-20,20,20,0,-10,
-10,0,-10,-5,5,10,-5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,80,-20,0,0,0,-10,0,-20,20,0,5,-5,5,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[100,0,0,4,0,0,0,0,4,4,0,
0,0,0,0,0,-25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,-5,0,4,0,0,-1,0,0,0,-1,0,-1,0,0,0,
0,0,0,0,-1,-1,0,0,0,0,0],
[TENSOR,[51,4]],
[TENSOR,[51,3]],
[TENSOR,[51,2]],[200,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,-50,0,0,0,0,0,0,0,0,0,0,0,
0,0,10,-5,0,0,2,0,0,2,0,0,0,-3,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[200,0,0,-8,0,
0,0,0,0,0,0,0,0,0,0,0,-50,0,0,0,0,0,0,0,0,0,0,0,0,0,-10,0,5,0,2,0,0,2,0,0,0,2,
0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[55,2]],
[TENSOR,[56,2]]],
[( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(46,47)(48,49)(50,51)(52,53)(54,55)
(56,57)]);
ARC("LyN5","CAS",[rec(name:="lyn5",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("LyN5","HN.2",[1,3,3,3,48,48,8,8,48,48,48,48,8,8,48,48,10,10,10,11,11,
12,10,12,11,11,11,11,12,9,10,11,12,22,22,23,22,22,23,25,23,23,25,25,22,66,
66,66,66,37,37,66,66,37,37,66,66,40],[
"fusion map is unique"
]);
ALF("LyN5","Ly",[1,2,2,2,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,6,
7,7,6,7,7,15,15,15,15,15,15,16,16,16,16,16,16,26,26,26,26,26,26,26,26,26,
26,26,26,34],[
"fusion map is unique"
]);
ALF("LyN5","B",[1,5,5,5,17,17,17,17,17,17,17,17,17,17,17,17,19,19,19,19,
19,18,19,18,19,19,19,19,18,18,19,19,18,53,53,53,53,53,53,52,53,53,52,52,
53,108,108,108,108,108,108,108,108,108,108,108,108,128],[
"fusion map determined by factorization through HN.2"
]);
ALN("LyN5",["HN.2N5","BN5"]);

MOT("M11N2",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic Mathieu group M11"
],
[16,16,4,8,4,8,8],
[,[1,1,1,2,2,4,4]],
[[1,1,-1,1,-1,1,1],[1,1,-1,1,1,-1,-1],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[5,2]],[2,2,0,-2,0,0,0]],
[(6,7)]);
ARC("M11N2","CAS",[rec(name:="m11n2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("M11N2","M11",[1,2,2,4,4,7,8],[
"fusion is unique up to table automorphisms"
]);
ALF("M11N2","U3(5)",[1,2,2,4,4,12,13],[
"fusion is unique up to table automorphisms"
]);
ALF("M11N2","QD16.2",[1,2,8,4,10,6,6]);
ALF("M11N2","U3(5).2N2",[1,2,5,8,9,11,11],[
"fusion is unique up to table automorphisms"
]);
ALF("M11N2","A6.2_3",[1,2,2,4,6,7,8],[
"fusion map is unique up to table aut."
]);
ALN("M11N2",["M11Syl2","QD16"]);

MOT("M12N2",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic Mathieu group M12"
],
[64,64,32,16,16,16,16,8,32,32,16,16,16,16,8,8],
[,[1,1,1,1,1,1,1,1,2,2,3,3,2,2,10,9]],
[[1,1,1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1],[1,1,1,1,1,1,1,-1,1,1,-1,-1,1,1,-1,
-1],[1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,-1],[1,1,1,-1,-1,1,-1,1,1,1,-1,-1,1,
-1,-1,1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,-2,0,0,0,-2,0,-2,2,0,0,0,2,0,0],
[TENSOR,[9,1]],[2,2,-2,0,0,-2,0,0,2,-2,0,0,2,0,0,0],
[TENSOR,[11,1]],[2,2,2,-2,2,0,0,0,-2,-2,0,0,0,0,0,0],
[TENSOR,[13,3]],[4,-4,0,0,0,0,0,0,0,0,-2,2,0,0,0,0],
[TENSOR,[15,1]]],
[(11,12),(4,5),( 6, 7)( 9,10)(13,14)(15,16)]);
ARC("M12N2","CAS",[rec(name:="m12n2",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="p2(m12)",
permchars:=( 1, 8)( 2, 6, 5, 7, 3)( 9,10)(11,14)(12,13)(15,16),
permclasses:=( 4,10)( 5,11,14, 8, 6,12,15, 9),
text:=[
"names:=           p2[m12]\n",
" order:             2^6 = 64\n",
" number of classes: 16\n",
" source/origin:     pahlings,h.\n",
" comments:          p2(m12) is 2-sylow-subgroup of m12\n",
" test:              orth.1, min, sym(3)             \n",
""])]);
ALF("M12N2","M12",[1,3,3,3,2,2,2,3,7,6,7,6,7,6,11,12],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("M12N2","U3(3).2",[1,2,2,11,11,11,2,11,5,6,5,6,12,6,14,9],[
"compatible with M12C4 -> U3(3)"
]);
ALF("M12N2","G2(3)",[1,2,2,2,2,2,2,2,8,9,8,9,8,9,16,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("M12N2","G2(3).2N2",[1,2,3,5,4,7,7,13,6,6,14,14,8,8,17,17],[
"fusion map is unique up to table autom."
]);
ALN("M12N2",["G2(3)N2","M12Syl2","p2(m12)"]);

MOT("M12N3",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M12"
],
[108,12,12,12,54,18,18,9,6,6,6],
[,[1,1,1,1,5,6,7,8,7,6,5],[1,2,3,4,1,1,1,1,4,3,2]],
[[1,-1,-1,1,1,1,1,1,1,-1,-1],[1,-1,1,-1,1,1,1,1,-1,1,-1],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,0,-2,0,2,-1,2,-1,0,1,0],
[TENSOR,[5,1]],[2,0,0,-2,2,2,-1,-1,1,0,0],
[TENSOR,[7,2]],[4,0,0,0,4,-2,-2,1,0,0,0],[6,2,0,0,-3,0,0,0,0,0,-1],
[TENSOR,[10,1]]],
[( 3, 4)( 6, 7)( 9,10)]);
ARC("M12N3","CAS",[rec(name:="m12n3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("M12N3","M12",[1,3,3,3,4,4,4,5,10,10,10],[
"fusion map is unique"
]);
ALF("M12N3","3^(1+2):D8",[1,2,3,3,5,6,6,7,10,10,9],[
"fusion map is unique up to table autom."
]);
ALN("M12N3",["M12N3A"]);

MOT("M24N2",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic Mathieu group M24\n",
"Sylow 2 normalizer in sporadic Held group He"
],
[1024,1024,512,512,512,256,256,256,256,256,256,128,128,128,128,128,128,128,
128,128,128,64,64,64,64,64,128,128,128,128,128,128,64,64,64,64,64,64,64,64,64,
64,64,64,64,64,64,32,32,32,32,32,32,32,32,32,32,32,16,16,16],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5,5,3,5,5,
2,5,2,3,3,2,3,3,3,5,11,6,7,4,7,11,8,9,8,6,9,18,14,29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,1,
1,-1,-1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,
-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,1,-1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,1,-1,
1,-1,1,1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,
1,-1,1,1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,1],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,-1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,
1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,
1,1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[1,1,1,1,1,1,1,1,1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,
-1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,1,-1,
-1,-1,1,1,-1],
[TENSOR,[2,9]],
[TENSOR,[3,9]],
[TENSOR,[2,11]],
[TENSOR,[5,9]],
[TENSOR,[2,13]],
[TENSOR,[3,13]],
[TENSOR,[2,15]],[2,2,2,2,2,-2,2,-2,-2,-2,2,0,-2,2,0,0,2,-2,0,0,0,0,0,0,-2,0,
-2,2,2,0,-2,0,0,0,0,-2,0,0,2,-2,2,0,0,0,2,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,2]],
[TENSOR,[17,10]],
[TENSOR,[17,9]],[2,2,2,2,2,2,-2,2,2,2,-2,-2,0,2,-2,0,0,-2,-2,0,2,0,0,0,0,-2,0,
0,-2,-2,-2,2,2,2,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0],
[TENSOR,[21,3]],
[TENSOR,[21,5]],
[TENSOR,[21,7]],[2,2,2,2,2,2,-2,-2,2,-2,-2,0,0,-2,-2,0,0,2,0,0,2,0,-2,0,0,0,0,
0,2,-2,-2,2,0,0,0,0,2,-2,0,0,0,-2,0,2,0,0,2,0,2,0,0,0,0,0,-2,0,0,0,0,0,0],
[TENSOR,[25,3]],
[TENSOR,[25,4]],
[TENSOR,[25,2]],[2,2,2,2,2,-2,2,2,-2,2,2,0,2,-2,0,-2,-2,2,0,-2,0,-2,0,0,0,0,2,
-2,-2,0,-2,0,0,0,2,-2,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],
[TENSOR,[29,4]],[2,2,2,2,2,2,2,-2,2,-2,2,0,-2,-2,2,0,-2,-2,0,0,2,0,0,-2,0,0,
-2,-2,-2,2,2,2,0,0,0,2,0,0,2,0,0,-2,-2,-2,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,3]],
[TENSOR,[33,4]],
[TENSOR,[33,2]],[4,4,-4,-4,4,0,-4,0,0,0,4,-2,4,0,0,0,0,0,-2,0,0,0,-2,0,0,2,-4,
0,0,0,0,0,-2,2,0,0,2,2,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,2]],[4,4,-4,-4,4,0,4,0,0,0,-4,2,0,0,0,0,-4,0,2,0,0,0,-2,0,0,-2,0,
4,0,0,0,0,-2,2,0,0,-2,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,2]],
[TENSOR,[37,5]],
[TENSOR,[37,6]],
[TENSOR,[39,6]],
[TENSOR,[39,5]],[4,4,4,-4,-4,-4,0,0,4,0,0,0,0,0,0,-2,0,0,0,-2,-4,2,0,0,2,0,0,
0,0,0,0,4,0,0,-2,0,0,0,0,-2,2,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[45,3]],
[TENSOR,[45,4]],
[TENSOR,[45,2]],[4,4,4,4,4,-4,-4,-4,-4,-4,-4,0,0,4,0,0,0,4,0,0,0,0,0,0,0,0,0,
0,-4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,
4,4,-4,-4,4,-4,4,-4,0,0,-4,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,4,0,4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,-4,-4,4,0,0,-4,0,0,0,0,0,
4,2,0,0,0,2,0,-2,0,0,2,0,0,0,0,-4,0,0,0,0,-2,0,0,0,0,-2,-2,0,0,0,2,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[51,3]],
[TENSOR,[51,4]],
[TENSOR,[51,2]],[8,-8,0,0,0,0,0,4,0,-4,0,-4,0,0,0,4,0,0,4,-4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,0],
[TENSOR,[55,5]],
[TENSOR,[55,2]],
[TENSOR,[55,6]],[8,8,-8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[59,2]],[16,-16,0,0,0,0,0,-8,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(16,20)(54,56),(12,19)(54,56),( 7,11)(13,17)(27,28)(33,34)(36,39)(37,47)
(48,50)(52,53),( 3, 5)( 6, 7)( 9,11)(12,16)(13,21)(14,18)(15,17)(19,20)(22,26)
(23,25)(27,32)(28,30)(33,35)(34,46)(36,44)(37,45)(38,40)(39,42)(41,47)(48,55)
(49,50)(52,57)(53,58)(59,60)]);
ARC("M24N2","CAS",[rec(name:="m24n2",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="hen2",
permchars:=( 1, 2, 8,12,10, 9,15, 3)( 4, 7,14, 6,11,16, 5,13)(17,35,23,26,30,
 20,33,22,28,31,18,36,24,25,29)(19,34,21,27,32)(37,49,53,39,45,43,51,42,47)
(38,50,54,40,46,44,52,41,48),
permclasses:=( 3, 4)( 6, 7, 9, 8,11,10)(13,19,17,20,16,15,18)(22,23,25,26)
(27,30,29)(28,31)(33,34,37,47,44,45,38,41,46)(35,36,40,43)(48,52,58,57,55,53,
 56,54)(49,50,51),
text:="")]);
ALF("M24N2","M24",[1,2,2,3,2,2,2,2,3,3,3,2,3,2,2,3,2,3,3,2,3,3,3,3,2,2,6,
6,7,6,6,6,7,6,6,6,6,7,7,7,6,6,6,7,7,7,7,8,6,7,8,6,8,6,8,7,7,8,8,7,14],[
"computed from the groups"
]);
ALF("M24N2","He",[1,3,3,2,3,3,3,3,2,2,2,2,2,3,3,2,3,3,3,3,2,3,3,2,3,3,7,7,
8,7,7,7,7,8,7,8,8,8,7,8,7,7,7,8,8,8,7,6,7,7,6,8,6,7,6,8,8,6,8,8,17],[
"computed from the groups"
]);
ALN("M24N2",["HeN2"]);

MOT("McLN2",
[
"origin: Ostermann, tests: 1.o.r., pow[2],\n",
"2nd power map determined only up to matrix automorphisms,\n",
"Sylow 2 normalizer in sporadic McLaughlin group McL,\n",
"Sylow 2 subgroup of 2.A8,"
],
0,
0,
0,
0,
["ConstructPermuted",["2^4:D8"],(6,7,8)(10,11,13,12)(15,16),(1,2,7,5,6,3)(4,8)
(9,11,10,12)(15,16)]);
ARC("McLN2","CAS",[rec(name:="mcn2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("McLN2","McL",[1,2,2,2,2,2,2,2,5,5,5,5,5,5,5,5,12]);
ALF("McLN2","2.A8",[1,2,3,3,3,3,3,3,4,9,4,4,9,9,9,9,10]);
ALF("McLN2","LyN2",[1,2,3,5,5,11,7,11,4,16,8,6,16,13,19,19,17],[
"fusion map is unique"
]);
ALN("McLN2",["(2.A8)Syl2"]);

MOT("RuN2",
[
"origin: Ostermann\n",
"Sylow 2 normalizer in sporadic Rudvalis group Ru,\n",
"2nd power map is not determined by the characters,"
],
[16384,16384,8192,4096,2048,1024,1024,512,512,256,256,256,256,256,128,128,1024
,512,512,512,512,512,512,512,512,512,512,512,512,256,256,256,256,256,256,256,
256,256,256,256,256,256,256,256,256,256,256,256,256,256,128,128,128,128,128,
128,128,128,128,64,64,64,64,64,64,64,32,32,32,64,32,32,32,32,32,32,32,32,32,32
,32,32,16,16,16],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,3,4,2,4,2,4,3,2,3,3,4,4,4,3,3,4,4,3,4,
4,4,4,2,4,4,3,4,4,4,3,2,2,7,5,5,7,3,7,2,7,5,8,6,6,7,5,6,8,11,9,11,17,19,18,21,
24,22,23,27,20,25,26,28,29,52,70,70]],
[[1,1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,
1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,
-1,-1,1,1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,1,1,1,1,1,-1,-1],[1,1,1,1,1,1,1,1,1,-1,
1,-1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,1,-1,1,
-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,1,1,1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,
-1,-1,-1,1,1,-1,1,-1,-1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,
-1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,1,1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,1,1,
-1,1,1,-1,1,-1,1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,2,2,2,2,2,-2,0,2,0,-2,0,-2,0,2,2,2,2,2,-2,2,2,2,-2,2,2,
-2,-2,0,0,0,2,-2,-2,0,0,0,2,-2,0,-2,0,0,0,0,0,0,2,-2,2,0,0,-2,0,0,-2,0,0,2,-2,
0,-2,-2,0,0,0,0,-2,2,0,0,0,0,2,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,1]],[2,2,2,2,2,2,2,2,2,-2,-2,-2,2,-2,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,-2,-2,-2,2,2,2,-2,-2,-2,2,2,-2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,-2,0,
0,-2,0,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,2,0,0,0,0,0,0,0,0],
[TENSOR,[11,1]],[2,2,2,2,2,2,2,2,-2,0,-2,0,-2,0,0,0,2,2,2,2,2,-2,2,2,2,-2,2,2,
-2,-2,0,0,0,2,-2,-2,0,0,0,2,-2,0,-2,0,0,0,0,0,0,-2,2,-2,0,0,0,0,0,2,0,2,-2,0,
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[TENSOR,[13,3]],[2,2,2,2,2,2,2,-2,2,0,2,0,-2,0,0,-2,2,2,2,2,-2,2,2,2,-2,2,2,
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[TENSOR,[15,1]],[2,2,2,2,2,2,2,-2,-2,0,2,0,2,0,0,0,2,2,2,2,-2,-2,2,2,-2,-2,2,
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0,0,0,0,0,2,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0],
[TENSOR,[17,2]],[2,2,2,2,2,2,2,-2,2,0,-2,0,-2,0,0,0,2,2,2,2,-2,2,2,2,-2,2,2,
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[TENSOR,[19,2]],[2,2,2,2,2,2,2,-2,-2,0,-2,0,2,0,0,0,2,2,2,2,-2,-2,2,2,-2,-2,2,
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0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(4),-2*E(4)],
[TENSOR,[21,1]],[4,4,4,4,4,4,-4,0,0,-2,0,2,0,2,-2,0,-4,0,0,4,4,0,0,-4,0,0,0,4,
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0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0],[4,4,4,4,4,4,-4,4,0,-2,0,2,0,
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0],
[TENSOR,[23,5]],
[TENSOR,[24,5]],[4,4,4,4,4,4,4,0,-4,0,0,0,0,0,-2,0,4,-4,4,-4,0,4,4,-4,0,-4,-4,
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[TENSOR,[23,3]],
[TENSOR,[24,3]],
[TENSOR,[23,1]],
[TENSOR,[24,1]],
[TENSOR,[27,1]],
[TENSOR,[28,1]],[4,4,4,4,4,-4,4,0,0,-2,0,2,0,2,0,-2,-4,0,-4,0,0,4,4,0,0,0,0,0,
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0,0],
[TENSOR,[35,3]],
[TENSOR,[36,3]],[4,4,4,4,4,4,4,0,0,-2,-4,-2,0,2,0,0,4,4,-4,-4,0,0,-4,-4,0,0,4,
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0,0,0,0,0,0,0,0,0,2,0,0,0,0,-2,0,0,0,0,0,0,0,0],[4,4,4,4,4,4,4,0,0,-2,4,-2,0,
2,0,0,4,4,-4,-4,0,0,-4,-4,0,0,4,0,0,0,2,-2,-2,0,0,0,2,2,2,0,0,-2,0,2,-2,-2,-2,
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0],
[TENSOR,[35,2]],
[TENSOR,[36,2]],
[TENSOR,[35,1]],
[TENSOR,[36,1]],
[TENSOR,[39,1]],
[TENSOR,[40,1]],[4,4,4,4,4,4,4,-4,0,0,0,0,0,0,0,-2,4,-4,-4,4,4,0,-4,4,-4,0,-4,
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0,0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0],[4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,-2,
4,-4,-4,4,-4,0,-4,4,4,0,-4,-4,0,0,0,0,0,4,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[47,1]],
[TENSOR,[48,1]],[8,8,8,8,-8,0,0,4,4,-6,0,-2,0,2,0,0,0,4,0,0,4,4,0,0,-4,-4,-4,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[51,1]],[8,8,8,8,8,-8,-8,0,0,-4,0,-4,-4,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[53,1]],[8,8,8,8,-8,0,0,-4,-4,-2,0,-6,0,-2,0,0,0,4,0,0,-4,-4,0,0,4,4,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,-4,-4,-2,0,2,
-4,-6,0,0,0,-4,0,0,4,4,0,0,4,4,4,-4,-4,0,-2,2,-2,0,0,4,2,6,2,0,0,2,0,2,-2,2,
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0,0],[8,8,8,8,-8,0,0,-4,4,-2,0,2,0,-2,0,0,0,4,0,0,-4,4,0,0,4,-4,-4,4,-4,-4,2,
2,6,0,0,0,-2,2,-2,0,0,2,4,-2,-2,-6,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,-4,4,-2,0,2,4,2,0,0,0,-4,
0,0,4,-4,0,0,4,-4,4,-4,4,0,-2,2,-2,0,0,-4,2,-2,-6,0,0,2,0,2,-2,2,-2,-2,6,0,0,
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0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,4,-4,-2,0,2,4,2,0,0,0,-4,0,0,-4,4,0,0,
-4,4,4,4,-4,0,6,2,-2,0,0,-4,2,-2,2,0,0,2,0,-6,-2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,0,4,4,-2,
0,2,-4,2,0,0,0,-4,0,0,-4,-4,0,0,-4,-4,4,4,4,0,-2,2,-2,0,0,4,-6,-2,2,0,0,2,0,2,
-2,2,-2,6,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[55,1]],
[TENSOR,[56,1]],
[TENSOR,[57,1]],
[TENSOR,[58,1]],
[TENSOR,[59,1]],
[TENSOR,[60,1]],
[TENSOR,[61,1]],[8,8,8,8,8,8,-8,-8,0,0,0,0,0,0,0,0,-8,0,0,-8,0,0,0,8,-8,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,-8,8,0,-8,0,0,0,0,0,0,0,-8,0,
8,0,0,0,-8,0,0,-8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,-8,-8,0,
0,0,0,0,4,4,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,0,0,0,0,4,4,4,-4,0,0,0,-4,-4,
0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],
[TENSOR,[71,1]],[8,8,8,8,8,-8,8,0,0,0,0,0,0,0,0,0,-8,0,-8,0,0,-8,8,0,0,0,0,0,
-8,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,8,-8,0,0,0,0,0,0,0,0,0,-8,0,
0,8,-8,0,0,-8,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,-16,0,
0,0,0,0,0,4,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-4,0,0,0,-4,4,4,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[75,5]],
[TENSOR,[75,1]],
[TENSOR,[75,2]],[32,32,-32,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,-4,0,0,0,4,4,4,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[32,32,-32,0,0,0,0,0,0,0,0,0,0,0,0,-4,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,4,0,0,
0,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[79,1]],
[TENSOR,[80,1]],[32,32,32,-32,0,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[64,-64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-4,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[84,3]]],
[(84,85),(60,66),(54,56)(67,69),(51,58)(53,59)]);
ARC("RuN2","CAS",[rec(name:="run2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("RuN2","Ru",[1,2,2,2,2,2,2,2,2,2,2,3,3,3,2,2,7,8,8,5,8,8,5,8,7,7,5,5,
5,7,8,7,8,8,8,8,5,7,6,6,6,8,6,6,8,7,6,6,8,7,8,8,5,8,7,5,7,5,8,8,7,8,8,7,7,
5,8,7,7,14,15,15,15,15,15,13,13,13,14,14,13,13,15,25,26]);

MOT("(2^2xD14):3",
[
"Sylow 7 normalizer in Ru,\n",
"of structure (2^2xD14):3, subdirect product of A4 and 7:6,\n",
"contained in maximal subgroups of type (2^2xSz(8)):3,\n",
"origin: Dixon's Algorithm"
],
[168,28,24,28,28,8,28,56,6,6,6,6],
[,[1,2,1,2,2,1,2,1,11,11,9,9],[1,2,3,7,4,6,5,8,1,3,1,3],,,,[1,1,3,8,8,6,8,8,9,
10,11,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,E(3),E(3),E(3)^2,E(3)^2],
[TENSOR,[2,2]],[3,3,3,-1,-1,-1,-1,-1,0,0,0,0],[1,1,-1,1,1,-1,1,1,1,-1,1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[4,5]],[6,-1,0,-1,-1,0,-1,6,0,0,0,0],[6,-1,0,
E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^5+E(7)^6,
-E(7)+E(7)^2-E(7)^3-E(7)^4+E(7)^5-E(7)^6,0,
-E(7)-E(7)^2+E(7)^3+E(7)^4-E(7)^5-E(7)^6,-2,0,0,0,0],
[GALOIS,[10,2]],
[GALOIS,[10,3]]],
[(9,11)(10,12),(4,5,7)]);
ALF("(2^2xD14):3","Ru",[1,12,2,21,23,3,22,3,4,11,4,11],[
"fusion map is unique up to table automorphisms"
]);
ALF("(2^2xD14):3","R(27)",[1,8,2,18,20,2,19,2,4,6,5,7],[
"fusion map is unique up to table aut."
]);
ALN("(2^2xD14):3",["RuN7","R(27)M5","R(27)N7"]);

MOT("(2^2x13:4):3",
[
"Sylow 13 normalizer in Ru,\n",
"of structure (2^2x13:4):3, subdirect product of A4 and 13:12,\n",
"contained in maximal subgroups of type (2^2xSz(8)):3,\n",
"origin: Dixon's Algorithm"
],
[624,208,52,52,52,52,16,48,16,48,48,16,12,12,12,12,12,12,12,12],
[,[1,1,3,3,3,3,1,1,8,8,8,8,14,13,13,14,15,16,15,16],[1,2,3,5,6,4,7,8,12,11,10,
9,1,1,8,8,11,11,10,10],,,,,,,,,,[1,2,1,2,2,2,7,8,9,10,11,12,13,14,15,16,17,18,
19,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,E(3),
E(3)^2,E(3)^2,E(3),E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[2,4]],
[TENSOR,[2,5]],[1,1,1,1,1,1,-1,-1,-E(4),-E(4),E(4),E(4),1,1,-1,-1,-E(4),-E(4)
,E(4),E(4)],
[TENSOR,[2,7]],
[TENSOR,[2,8]],
[TENSOR,[4,7]],
[TENSOR,[2,10]],
[TENSOR,[2,11]],[12,12,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,-1,3,-1,-1
,-1,-1,3,-1,3,3,-1,0,0,0,0,0,0,0,0],
[TENSOR,[14,4]],
[TENSOR,[14,7]],
[TENSOR,[14,10]],[12,-4,-1,
-E(13)-E(13)^2-E(13)^3+E(13)^4-E(13)^5+E(13)^6+E(13)^7-E(13)^8+E(13)^9
-E(13)^10-E(13)^11-E(13)^12,
E(13)-E(13)^2-E(13)^3-E(13)^4+E(13)^5-E(13)^6-E(13)^7+E(13)^8-E(13)^9-E(13)^10
 -E(13)^11+E(13)^12,
-E(13)+E(13)^2+E(13)^3-E(13)^4-E(13)^5-E(13)^6-E(13)^7-E(13)^8-E(13)^9
+E(13)^10+E(13)^11-E(13)^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[18,4]],
[GALOIS,[18,2]]],
[( 4, 5, 6),(13,14)(15,16)(17,18)(19,20),( 9,12)(10,11)(17,19)(18,20)]);
ALF("(2^2x13:4):3","Ru",[1,3,20,32,33,34,3,2,8,6,6,8,4,4,11,11,19,19,19,
19],[
"fusion map determined by factorization through (2^2xSz(8)):3"
]);
ALN("(2^2x13:4):3",["RuN13"]);

MOT("SuzN2",
[
"origin: Ostermann\n",
"Sylow 2 normalizer in sporadic Suzuki group Suz,\n",
"used the group for determining the 2nd power map"
],
[24576,24576,12288,6144,3072,1536,768,768,512,256,256,256,128,384,384,1536,
1024,1024,768,768,768,768,768,512,512,512,384,256,256,256,256,256,256,256,128,
128,128,96,32,384,384,192,192,96,96,96,96,48,48,48,48,48,48,96,64,64,64,64,64,
64,32,32,32,96,96,48,48,48,48,48,48,48,48,48,48,24,24,24,24,24,24],
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4,6,9,14,15,14,15,14,15,15,14,14,15,14,15,14,15,16,17,18,18,17,17,18,26,24,25,
40,41,40,41,40,41,42,43,42,43,43,42,44,45,47,46,65,64],[1,2,3,4,5,6,7,8,9,10,
11,12,13,1,1,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
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22,21,21,20,20,19,19,23,23,38,38,27,27,54,54]],
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[TENSOR,[13,3]],
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[TENSOR,[16,7]],
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[TENSOR,[20,7]],
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[TENSOR,[34,2]],[6,6,6,6,6,-6,0,0,-6,0,6,0,-2,0,0,-6,6,6,-6,0,0,0,0,-6,6,6,0,
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[TENSOR,[39,2]],[8,8,8,8,-8,-8,0,0,0,0,0,0,0,2*E(3),2*E(3)^2,-8,-8,8,8,0,0,0,
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[TENSOR,[41,5]],
[TENSOR,[41,3]],[8,8,8,-8,0,4,0,-6,-4,0,0,2,0,2*E(3)^2,2*E(3),-4,0,0,0,6,0,2,
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2*E(3)^2,2*E(3),0,0,0,0,0,0,-2*E(3),-2*E(3)^2,0,0,0,0,0,0],
[TENSOR,[44,1]],[8,8,8,-8,0,-4,0,-2,4,0,0,-2,0,2*E(3)^2,2*E(3),4,0,0,0,2,0,6,
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[TENSOR,[46,1]],
[TENSOR,[44,5]],
[TENSOR,[44,11]],
[TENSOR,[46,5]],
[TENSOR,[46,11]],
[TENSOR,[44,3]],
[TENSOR,[44,9]],
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[TENSOR,[57,1]],
[TENSOR,[56,1]],[12,12,12,12,-12,0,0,-6,4,-4,0,-2,0,0,0,0,4,-4,0,-6,0,6,6,4,0,
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[TENSOR,[60,2]],
[TENSOR,[60,7]],
[TENSOR,[60,1]],[16,16,-16,0,0,0,-4,0,0,4,0,0,0,4*E(3)^2,4*E(3),0,0,0,0,0,4,0,
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0,0,0,0,0,0,0,0],
[TENSOR,[64,2]],
[TENSOR,[64,5]],
[TENSOR,[64,6]],
[TENSOR,[64,3]],
[TENSOR,[64,4]],[24,24,24,24,24,0,0,0,0,0,8,0,0,0,0,0,-8,-8,0,0,0,0,0,0,-8,-8,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,24,24,-24,0,0,0,-8,0,0,0,0,0,0,0,8,-8,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,24,-24,0,12,0,6,4,0,
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[TENSOR,[72,1]],[24,24,24,-24,0,-12,0,6,-4,0,0,-2,0,0,0,12,0,0,0,-6,0,6,-6,4,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[74,1]],[32,-32,0,0,0,0,0,0,0,0,0,0,0,8*E(3)^2,8*E(3),0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[76,5]],
[TENSOR,[76,3]],[48,48,-48,0,0,0,-12,0,0,-4,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[79,2]],[96,-96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(55,58),(14,15)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(64,65)
(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)]);
ALF("SuzN2","Suz",[1,2,2,2,2,2,2,2,3,3,3,3,3,4,4,7,8,7,9,9,7,9,7,9,7,8,9,
8,8,7,8,8,9,9,7,8,8,9,10,13,13,13,13,13,13,13,13,13,13,13,13,13,13,19,20,
19,19,20,20,19,20,21,19,27,27,29,29,27,27,29,29,29,29,27,27,29,29,29,29,
43,43],[
"fusion map is unique"
]);

MOT("ThN2",
[
"origin: Ostermann\n",
"Sylow 2 normalizer in sporadic Thompson group Th,\n",
"power map computed from the group"
],
[32768,32768,16384,8192,4096,2048,2048,1024,1024,512,512,512,256,256,256,256,
2048,1024,1024,512,512,512,512,512,512,512,512,256,256,256,256,256,256,256,
256,256,256,256,256,256,256,256,256,256,128,128,128,128,128,128,128,64,64,64,
64,64,64,64,64,64,64,32,32,32,128,128,128,128,128,128,128,64,64,64,64,64,64,
32,32,32,32,32,32,32,32,32,32,16,16],
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18,19,18,18,19,19,20,21,22,23,31,24,31,26,25,27,46,47]],
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[]);
ARC("ThN2","CAS",[rec(name:="thn2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("ThN2","Th",[1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,6,6,6,6,6,6,7,7,7,7,7,7,
7,7,7,7,6,7,7,7,7,6,7,7,7,6,7,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,
14],[
"fusion map is unique"
]);

MOT("ThN3",
[
"Sylow 3 normalizer in Th,\n",
"origin: Dixon's Algorithm"
],
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162,81,162,162,162,108,108,108,108,108,108,54,54,54,54,54,54,54,54,54,18,18,18
,486,243,243,243,243,162,81,18,18,18,18,18,18,27,27,27],
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[TENSOR,[24,3]],[6,6,6,6,6,6,6,-3,6,6,6,-3,6,-3,-3,-3,6,-3,6,-3,0,0,0,0,0,0,0
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[TENSOR,[26,3]],[12,12,12,12,12,12,12,-6,-6,-6,-6,3,-6,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[33,2]],
[TENSOR,[32,2]],
[TENSOR,[31,2]],[12,12,12,12,12,12,-6,0,12,12,12,0,-6,-6,-6,-6,0,3,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[41,2]],
[TENSOR,[41,4]],
[TENSOR,[42,4]],
[TENSOR,[41,3]],
[TENSOR,[42,3]],
[TENSOR,[41,2]],
[TENSOR,[42,2]],[18,18,18,-9,0,0,0,0,9,0,-9,0,0,0,0,0,6,0,-3,0,0,0,0,6,-3,6,
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[TENSOR,[49,2]],[36,36,36,-18,0,0,0,0,18,0,-18,0,0,0,0,0,-6,0,3,0,0,0,0,12,-6
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[GALOIS,[53,2]],[54,54,54,-27,0,0,0,0,-27,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[55,2]],[54,54,54,-27,0,0,0,0,0,-27,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0],
[TENSOR,[57,2]],[54,54,-27,0,0,0,0,0,0,0,0,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,0,0,0,0,0],
[TENSOR,[59,3]],[54,54,-27,0,0,0,0,0,0,0,0,0,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,0,0,0,0,0],
[TENSOR,[61,3]],[54,54,-27,0,0,0,0,0,0,0,0,0,0,9,0,-9,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,0,0,0,0,0],
[TENSOR,[63,3]],[108,108,-54,0,0,0,0,0,0,0,0,0,0,-18,18,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0],[108,108,-54,0,0,0,0,0,0,0,0,0,0,0,-18,18,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,-6,3,3,
0,0,0,0,0,0,0,0,0,0,0],[108,108,-54,0,0,0,0,0,0,0,0,0,0,18,0,-18,0,0,0,0,0,0,0
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,3,0,0,0,0,0,0,0,0,0,0,0],[162,-81,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,
0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[162,-81,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9,0,9,0
,0,0,0,0,0,0,0,-6,0,0,0,0,3,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],[162,-81,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,0,0,
0,0,0,0,0,0,0,-6,0,0,0,0,3,0,0,0,0,0,0,0,0,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[70,2]],
[TENSOR,[69,2]],
[TENSOR,[68,2]]],
[(72,73),(27,28),(21,22,23)(46,47,48),(14,15,16)(52,54,53)(59,60,61),
( 5, 6)(40,41)(42,43)(44,45)]);
ALF("ThN3","Th",[1,4,4,4,3,3,15,4,3,4,5,5,16,3,4,5,15,16,16,17,3,5,4,4,5,
4,5,5,17,16,17,2,2,2,4,5,11,11,11,10,10,10,10,10,10,9,11,10,9,11,10,9,11,
10,11,11,11,15,16,16,15,16,17,17,27,28,28,27,28,27,36,37,38],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.HSN3",
[
"origin: Dixon's Algorithm",
"Sylow 3 normalizer in 2.HS"
],
[576,576,288,72,72,72,72,64,64,32,32,32,16,8,8,48,48,48,48,24,24,16,16,16,16,
24,24],
[,[1,1,2,4,4,5,5,1,1,2,8,8,9,8,8,1,1,2,2,4,4,12,12,12,12,5,5],[1,2,3,1,2,3,3,
8,9,10,11,12,13,14,15,16,17,19,18,17,16,22,23,24,25,19,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,
2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,0,0],
[TENSOR,[6,2]],[8,8,8,-1,-1,-1,-1,0,0,0,0,0,0,0,0,2,2,2,2,-1,-1,0,0,0,0,-1,
-1],
[TENSOR,[8,2]],[1,1,-1,1,1,-1,-1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,
1,1],
[TENSOR,[10,4]],
[TENSOR,[2,11]],
[TENSOR,[2,10]],
[TENSOR,[5,10]],
[TENSOR,[6,10]],
[TENSOR,[6,11]],
[TENSOR,[8,12]],
[TENSOR,[8,10]],[2,-2,0,2,-2,0,0,2,-2,0,-2,2,0,0,0,2,-2,0,0,-2,2,0,0,0,0,0,0],
[TENSOR,[19,2]],[2,-2,0,2,-2,0,0,2,-2,0,2,-2,0,0,0,0,0,-2*E(4),2*E(4),0,0,0,0,
0,0,-2*E(4),2*E(4)],
[TENSOR,[21,2]],[4,-4,0,4,-4,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,
-8,0,-1,1,-3*E(4),3*E(4),0,0,0,0,0,0,0,0,2,-2,2*E(4),-2*E(4),1,-1,0,0,0,0,
-E(4),E(4)],
[TENSOR,[24,10]],
[TENSOR,[24,12]],
[TENSOR,[24,2]]],
[(22,23)(24,25),(16,17)(18,19)(20,21)(26,27),( 6, 7)(18,19)(26,27),(14,15)
(22,24)(23,25)]);
ALF("2.HSN3","D8",[1,2,3,1,2,3,3,1,2,3,2,1,3,4,5,1,2,3,3,2,1,5,5,4,4,3,3]);
ALF("2.HSN3","s2wrs2",[1,2,5,1,2,5,5,1,2,5,2,1,5,4,3,1,2,5,5,2,1,3,3,4,4,
5,5]);
ALF("2.HSN3","3^2:Q8.2",[1,1,1,4,4,4,4,2,2,2,5,5,5,6,6,3,3,3,3,7,7,8,9,8,
9,7,7]);
ALF("2.HSN3","2x(3^2.QD16)",[1,1,2,7,7,12,12,3,3,4,9,9,8,10,11,5,5,6,6,14,
14,15,16,17,18,13,13],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.HSN3","2.HS",[1,2,5,6,7,18,19,3,4,5,11,11,10,11,11,3,4,5,5,21,20,
26,26,27,27,19,18],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.HSN3","2.HS.2N3",[1,2,12,11,20,35,35,4,5,13,14,15,17,19,19,6,7,16,
16,24,23,33,34,33,34,36,36],[
"fusion map is unique up to table automorphisms"
]);

MOT("5:4",
[
"2nd maximal subgroup of A5.2,\n",
"constructions: AGL(1,5)"
],
0,
0,
0,
[(3,5)],
["ConstructPermuted",["P:Q",[5,4]]]);
ARC("5:4","tomfusion",rec(name:="5:4",map:=[1,4,3,2,3],text:=[
"fusion map is unique"
]));
ALF("5:4","5:4x3",[1,4,7,10,13],[
"fusion map is unique up to table aut."
]);
ALF("5:4","A5.2",[1,4,6,2,6],[
"fusion map is unique"
]);
ALF("5:4","A6.2_3",[1,5,6,2,6],[
"fusion map uniquely determined by Brauer tables"
]);
ALF("5:4","M11",[1,5,4,2,4],[
"fusion map is unique"
]);
ALF("5:4","M22",[1,6,5,2,5],[
"determined by factorizing through A7 (the group contains 4B elements)"
]);
ALF("5:4","Sz(8)",[1,5,3,2,4],[
"fusion map is unique up to table autom."
]);
ALF("5:4","U4(2)",[1,10,9,3,9],[
"fusion map is unique"
]);
ALF("5:4","A7",[1,6,5,2,5],[
"fusion map is unique"
]);
ALF("5:4","A6.2_1",[1,6,9,2,9],[
"determined using that 5:4 is not contained in A6"
]);
ALF("5:4","2x5:4",[1,2,3,4,5],[
"fusion map is unique up to table aut."
]);
ALF("5:4","L3(4).2_1",[1,7,10,2,10],[
"fusion map determined using that L3(4) does not contain 5:4"
]);
ALF("5:4","L3(4).2_2",[1,6,10,2,10],[
"fusion map determined by the fact that 5:4 is not contained in L3(4)"
]);
ALF("5:4","U4(3)",[1,9,8,2,8],[
"fusion map determined by factorization through A7"
]);
ALN("5:4",["A7N5","AGL(1,5)","L3(4).2_1N5","L3(4).2_2N5","M11N5","M22N5",
"Sz(8)N5","U4(2)N5","U4(3)N5"]);

MOT("2x5:4",
0,
0,
0,
0,
[(3,8)(5,10),(3,5)(8,10)],
["ConstructDirectProduct",[["Cyclic",2],["5:4"]]]);
ALF("2x5:4","M12",[1,8,6,3,6,2,13,7,2,7],[
"fusion map is unique up to table automorphisms"
]);
ALF("2x5:4","2.Sz(8)",[1,6,4,3,5,2,7,4,3,5],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x5:4","2.M22",[1,10,9,4,9,2,11,9,3,9],[
"fusion map determined via the fusion 5:4 -> M22"
]);
ALF("2x5:4","A7.2",[1,6,5,2,5,9,14,11,10,11],[
"fusion map is unique up to table aut."
]);
ALF("2x5:4","M22.2",[1,6,5,2,5,13,18,15,13,15],[
"determined by the embedding of 5:4 (contains 4B elements)"
]);
ALF("2x5:4","U4(2).2",[1,9,8,3,8,16,24,19,17,19],[
"determined using that the outer order 4 elements have centralizer order 32"
]);
ALF("2x5:4","U4(3).2_1",[1,9,8,2,8,20,28,22,20,22],[
"determined using the factorization through U4(2).2"
]);
ALF("2x5:4","U4(3).2_2",[1,9,8,2,8,19,30,22,20,22],[
"determined using the factorization through S7"
]);
ALF("2x5:4","U4(3).2_3",[1,8,7,2,7,16,22,17,16,17],[
"determined using that 5:4 < U4(3) contains 4B elements"
]);
ALN("2x5:4",["2.M22N5","2.Sz(8)N5","M12N5","M22.2N5","U4(2).2N5",
"U4(3).2_1N5","U4(3).2_2N5","U4(3).2_3N5"]);

MOT("5:4x3",
0,
0,
0,
0,
[(2,3)(5,6)(8,9)(11,12)(14,15),(7,13)(8,14)(9,15)],
["ConstructDirectProduct",[["5:4"],["Cyclic",3]]]);
ALF("5:4x3","Sz(8).3",[1,8,9,5,16,17,3,12,13,2,10,11,4,14,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("5:4x3","3.M22",[1,2,3,14,15,16,11,12,13,4,5,6,11,12,13],[
"determined using the fusion 5:4 -> M22"
]);
ALF("5:4x3","3.A7",[1,2,3,12,13,14,9,10,11,4,5,6,9,10,11],[
"fusion map is unique up to table aut."
]);
ALF("5:4x3","3.A6.2_3",[1,2,3,11,12,13,14,15,16,4,5,6,14,15,16],[
"fusion map is unique up to table aut."
]);
ALN("5:4x3",["3.A7N5","3.M22N5"]);

MOT("6x5:4",
0,
0,
0,
0,
[(6,26)(7,27)(8,28)(9,29)(10,30)(11,21)(12,22)(13,23)(14,24)(15,25),
(3,5)(8,10)(13,15)(18,20)(23,25)(28,30),(3,18)(5,20)(8,23)(10,25)(13,
28)(15,30)],
["ConstructDirectProduct",[["Cyclic",6],["5:4"]]]);
ALF("6x5:4","5:4x3",[1,4,7,10,13,2,5,8,11,14,3,6,9,12,15,1,4,7,10,13,2,5,
8,11,14,3,6,9,12,15]);
ALF("6x5:4","2x5:4",[1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,
6,7,8,9,10]);
ALF("6x5:4","6.M22",[1,24,21,10,21,2,25,22,11,22,3,26,23,12,23,4,27,21,7,
21,5,28,22,8,22,6,29,23,9,23]);
ALN("6x5:4",["6.M22N5"]);

MOT("11:5",
[
"3rd maximal subgroup of L2(11)"
],
0,
0,
0,
[(2,3),(4,5,7,6)],
["ConstructPermuted",["P:Q",[11,5]]]);
ALF("11:5","HS",[1,19,20,10,10,10,10],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","L2(11)",[1,7,8,4,5,5,4],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","M11",[1,9,10,5,5,5,5],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","M12",[1,14,15,8,8,8,8],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","M22",[1,11,12,6,6,6,6],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","M23",[1,10,11,5,5,5,5],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","McL",[1,16,17,7,7,7,7],[
"fusion map is unique up to table automorphisms"
]);
ALF("11:5","U6(2)",[1,33,34,15,15,15,15],[
"fusion map is unique up to table aut."
]);
ALF("11:5","11:10",[1,2,2,4,6,8,10],[
"fusion map is unique up to table aut."
]);
ALF("11:5","2x11:5",[1,2,3,4,5,6,7],[
"fusion map is unique up to table aut."
]);
ALN("11:5",["HSN11","L2(11)N11","M11N11","M12N11","M22N11","M23N11",
"McLN11","U6(2)N11"]);

MOT("2x11:5",
0,
0,
0,
0,
[(2,3)(9,10),(4,5,7,6)(11,12,14,13)],
["ConstructDirectProduct",[["Cyclic",2],["P:Q",[11,5]]]]);
ALF("2x11:5","2.L2(11)",[1,12,14,6,8,8,6,2,13,15,7,9,9,7],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x11:5","Co3",[1,24,25,10,10,10,10,3,36,37,23,23,23,23],[
"fusion map is unique up to table automorphisms"
]);
ALF("2x11:5","2.M12",[1,23,25,12,12,12,12,2,24,26,13,13,13,13],[
"fusion map is unique up to table aut."
]);
ALF("2x11:5","2.HS",[1,31,33,16,16,16,16,2,32,34,17,17,17,17],[
"fusion map is unique up to table aut."
]);
ALF("2x11:5","2.M22",[1,20,22,10,10,10,10,2,21,23,11,11,11,11],[
"fusion map is unique up to table aut."
]);
ALF("2x11:5","Fi22",[1,36,37,14,14,14,14,2,61,62,34,34,34,34],[
"fusion map is unique up to table aut."
]);
ALF("2x11:5","McL.2",[1,14,15,7,7,7,7,20,30,31,25,25,25,25],[
"fusion map is unique up to table aut."
]);
ALN("2x11:5",["2.HSN11","2.M12N11","2.M22N11","Co3N11","Fi22N11"]);

MOT("17:8",
0,
0,
0,
0,
[(2,3),(4,6)(5,9)(8,10),(4,8)(6,10)],
["ConstructPermuted",["P:Q",[17,8]]]);
ALF("17:8","L2(17)",[1,11,10,5,4,6,2,6,4,5]);
ALF("17:8","J3",[1,18,19,9,5,9,2,9,5,9],[
"fusion map is unique up to table automorphisms"
]);
ALF("17:8","He",[1,26,27,17,8,17,3,17,8,17],[
"fusion map is unique up to table automorphisms"
]);
ALF("17:8","F4(2)",[1,80,81,48,23,48,5,48,23,48],[
"fusion map determined by the fact that class 4O is in the image"
]);
ALF("17:8","17:16",[1,2,2,4,6,8,10,12,14,16],[
"fusion map is unique up to table aut."
]);
ALN("17:8",["J3N17","HeN17","F4(2)N17"]);

MOT("17:16",
[
"constructions: AGL(1,17)"
],
0,
0,
0,
[(3,5,11,13)(4,8)(6,14)(7,17,15,9)(12,16),(3,7,11,15)(4,12)(5,17,13,9)(8,16)],
["ConstructPermuted",["P:Q",[17,16]]]);
ALF("17:16","L2(17).2",[1,10,13,5,14,4,16,6,15,2,15,6,16,4,14,5,13],[
"fusion map is unique up to table automorphisms"
]);
ALF("17:16","Fi23",[1,65,63,32,63,12,64,32,64,4,63,32,63,12,64,32,64],[
"fusion map is unique up to table automorphisms"
]);
ALF("17:16","F3+",[1,58,57,27,57,11,57,27,57,3,57,27,57,11,57,27,57],[
"fusion map is unique"
]);
ALF("17:16","He.2",[1,22,38,15,39,8,39,15,38,3,38,15,39,8,39,15,38],[
"fusion map is unique up to table aut."
]);
ALN("17:16",["AGL(1,17)","Fi23N17","F3+N17","He.2N17","L2(17).2M2"]);

MOT("19:9",
[
"1st maximal subgroup of L2(19)"
],
0,
0,
0,
[(2,3),(4,5,7,11,10,8)(6,9)],
["ConstructPermuted",["P:Q",[19,9]]]);
ALF("19:9","HN",[1,37,38,20,20,5,20,20,5,20,20],[
"fusion map is unique up to table automorphisms"
]);
ALF("19:9","J3",[1,20,21,10,11,4,12,12,4,11,10],[
"fusion map is unique up to table automorphisms"
]);
ALF("19:9","L2(19)",[1,11,12,6,7,3,8,8,3,7,6],[
"fusion map is unique up to table automorphisms"
]);
ALF("19:9","19:18",[1,2,2,4,6,8,10,12,14,16,18],[
"fusion map is unique up to table aut."
]);
ALF("19:9","U3(8).3_1",[1,13,14,29,30,5,29,30,5,29,30],[
"determined using that U3(8) does not contain 19:9"
]);
ALN("19:9",["HNN19","J3N19","L2(19)N19"]);

MOT("(3xD10).2",
[
"origin: Dixon's Algorithm"
],
[60,30,15,15,15,12,6,4,4],
[,[1,2,3,4,5,1,2,6,6],[1,1,3,3,3,6,6,9,8],,[1,2,1,2,2,6,7,8,9]],
[[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1],[1,1,1,1,1,-1,-1,E(4),-E(4)],
[TENSOR,[2,3]],[4,4,-1,-1,-1,0,0,0,0],[2,-1,2,-1,-1,-2,1,0,0],
[TENSOR,[6,3]],[4,-2,-1,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
E(15)+E(15)^2+E(15)^4+E(15)^8,0,0,0,0],
[GALOIS,[8,7]]],
[(4,5),(8,9)]);
ALF("(3xD10).2","S3",[1,2,1,2,2,1,2,3,3]);
ALF("(3xD10).2","5:4",[1,1,2,2,2,4,4,3,5]);
ALF("(3xD10).2","A8",[1,4,8,13,14,3,9,7,7],[
"fusion map is unique up to table aut."
]);
ALF("(3xD10).2","S3x5:4",[1,2,4,5,5,10,11,9,15],[
"fusion map is unique up to table aut."
]);
ALF("(3xD10).2","M23",[1,3,5,14,15,2,6,4,4],[
"fusion map is unique up to table automorphisms"
]);
ALN("(3xD10).2",["A8N5","M23N5"]);

MOT("7:3xS3",
0,
0,
0,
0,
[(4,7)(5,8)(6,9),(10,13)(11,14)(12,15)],
["ConstructDirectProduct",[["P:Q",[7,3]],["Dihedral",6]]]);
ALF("7:3xS3","M24",[1,5,2,12,23,19,13,24,20,4,5,10,4,5,10],[
"fusion map is unique up to table automorphisms"
]);
ALF("7:3xS3","3.M22.2",[1,2,23,14,15,31,16,17,32,5,5,27,5,5,27],[
"fusion map is unique up to table aut."
]);
ALN("7:3xS3",["M24N7"]);

MOT("S3x7:6",
0,
0,
0,
0,
[(3,7)(4,6)(10,14)(11,13)(17,21)(18,20)],
["ConstructDirectProduct",[["Dihedral",6],["P:Q",[7,6]]]]);
ARC("S3x7:6","tomfusion",rec(name:="7:6xS3",map:=[1,16,11,7,3,7,11,5,28,9,
6,14,6,9,4,22,13,12,2,12,13],text:=[
"fusion map is unique"]));
ALF("S3x7:6","Co3",[1,16,14,5,3,5,14,6,35,15,6,15,6,15,2,29,14,13,3,13,14],[
"fusion map is unique"
]);
ALF("S3x7:6","L3(4).D12",[1,6,9,3,7,3,9,12,15,17,12,17,12,17,19,23,25,21,
24,21,25],[
"fusion map is unique"
]);
ALF("S3x7:6","G2(4).2",[1,13,29,5,25,5,29,4,24,29,5,28,5,29,25,35,12,29,3,
29,12],[
"fusion map is unique"
]);
ALF("S3x7:6","Fi22",[1,26,22,7,4,7,22,5,60,25,8,20,8,25,2,51,24,19,4,19,
24],[
"fusion map is unique"
]);
ALN("S3x7:6",["Co3N7","Fi22N7"]);

MOT("(A4xD10).2",
[
"Sylow 5 normalizer in the sporadic simple Mathieu group M24,\n",
"origin: Dixon's Algorithm"
],
[240,80,30,60,20,15,15,48,16,6,8,8,8,8],
[,[1,1,3,4,4,6,7,1,1,3,8,8,9,9],[1,2,1,4,5,4,4,8,9,8,12,11,14,13],,[1,2,3,1,2,
3,3,8,9,10,11,12,13,14]],
0,
[(6,7),(11,12)(13,14)],
["ConstructIndexTwoSubdirectProduct","a4","Symm(4)","D10","5:4",[18,20,23,25],
(2,4)(3,8,6,9,7),(5,11,7)(8,13,9,12,10)]);
ALF("(A4xD10).2","Symm(4)",[1,2,3,1,2,3,3,1,2,3,4,4,5,5]);
ALF("(A4xD10).2","5:4",[1,1,1,2,2,2,2,4,4,4,3,5,3,5]);
ALF("(A4xD10).2","M24",[1,3,4,9,15,21,22,2,3,10,7,7,8,8],[
"fusion map is unique up to table automorphisms"
]);
ALN("(A4xD10).2",["M24N5"]);

MOT("Co2N2",
[
"origin: Dixon's Algorithm"
],
[262144,262144,131072,65536,32768,16384,65536,65536,32768,16384,16384,16384,
16384,16384,8192,8192,4096,8192,8192,8192,8192,2048,4096,16384,16384,8192,2048
,2048,4096,4096,2048,2048,4096,4096,2048,512,4096,4096,2048,2048,2048,32768,
32768,16384,8192,8192,8192,16384,16384,16384,16384,8192,8192,2048,4096,4096,
512,2048,2048,4096,4096,2048,4096,4096,2048,1024,2048,4096,4096,1024,1024,1024
,512,2048,4096,4096,1024,4096,4096,2048,1024,512,512,8192,8192,4096,2048,2048,
2048,1024,1024,512,512,512,512,1024,1024,2048,2048,1024,256,256,128,1024,1024,
512,512,512,512,512,512,512,64,1024,1024,512,512,1024,1024,2048,2048,1024,512,
2048,2048,1024,512,256,256,256,256,8192,8192,4096,2048,8192,8192,4096,2048,
4096,4096,2048,1024,1024,2048,2048,1024,1024,1024,1024,512,256,16384,16384,
8192,4096,2048,4096,4096,2048,2048,4096,4096,1024,1024,2048,2048,1024,1024,512
,2048,2048,1024,256,512,512,512,512,256,256,1024,1024,512,256,256,512,512,128,
128,128,128,512,512,256,256,256,256,256,256,256,512,512,256,128,128,128,1024,
2048,2048,1024,1024,2048,2048,1024,1024,1024,256,256,8192,8192,4096,2048,2048,
2048,2048,2048,2048,2048,2048,2048,1024,1024,1024,256,256,1024,1024,512,256,
256,256,256,256,256,256,256,256,128,128,128,128,128,64,1024,2048,2048,1024,
1024,1024,2048,2048,1024,1024,2048,2048,1024,1024,1024,2048,2048,1024,1024,
1024,256,256,256,256,256,256,256,512,512,256,256,256,256,64,64,2048,2048,1024,
512,1024,2048,2048,512,512,512,512,512,256,256,128,256,256,128,1024,2048,2048,
512,2048,2048,1024,512,256,256,64,128,128,128,128,64,4096,4096,2048,1024,2048,
4096,4096,1024,512,512,512,512,256,512,512,2048,4096,4096,1024,2048,4096,4096,
1024,256,512,512,1024,1024,512,512,512,128,512,512,512,512,256,256,128,128,128
,128,256,256,128,256,256,128,128,128,64,256,256,128,256,256,128,64,64,32,128,
128,64,256,256,128,256,256,128,64,64,32],
[,[1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,3,2,1,2,1,4,1,1,1,1,4,4,1,2,5,5,2,1,3,6,1,1
,4,4,3,1,1,1,1,1,2,1,1,1,1,3,3,3,4,4,6,5,5,2,1,3,3,3,1,4,7,8,8,7,11,11,14,8,7,
7,7,1,1,3,4,14,11,1,1,1,1,1,1,5,5,6,6,6,6,5,5,2,1,3,15,15,17,1,2,4,5,5,6,6,6,6
,22,6,6,5,5,6,6,1,2,4,6,1,2,4,6,19,21,18,20,1,1,3,4,1,1,3,4,3,3,1,4,4,4,4,1,3,
11,11,11,12,1,1,1,1,3,3,3,1,3,2,1,4,7,7,7,8,7,5,2,1,3,10,48,48,48,48,52,52,42,
42,42,45,45,42,43,55,55,46,47,19,19,18,18,19,12,11,13,14,24,24,24,23,29,30,1,4
,4,3,4,7,7,7,7,8,19,20,1,1,1,4,1,4,4,1,4,2,7,7,7,7,8,18,21,1,2,4,10,18,20,6,9,
19,21,24,25,23,30,29,38,38,41,4,1,1,3,4,7,8,8,7,7,7,7,7,8,7,4,4,3,1,4,18,21,20
,19,19,20,20,19,19,11,14,13,12,40,39,1,1,3,5,1,3,3,5,11,11,11,11,15,15,17,48,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[128,-128,0,0,0,0,-64,64,0,0,0,0,
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[TENSOR,[391,3]],[128,128,-128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-32,
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[393,2]]],
[(71,72)(132,136)(133,137)(134,138)(135,139)(149,150)(175,177)(176,178)(179,
180)(188,189)(192,193)(281,282)(297,298)(299,300)(323,344)(324,343)(325,342)
(326,345)(327,338)(328,340)(329,339)(330,341)(331,337)(332,336)(333,348)(334,
347)(335,346)(355,357)(356,358)(359,360)(363,364)(365,369)(366,368)(367,370)
(374,377)(375,378)(376,379)(380,381)(386,390)(387,389)(388,391)(392,393),(289,
290)(294,295)(301,302)(304,305)(308,309)(311,312)(323,324)(328,329)(333,334)
(339,340)(343,344)(347,348)(349,350)(355,356)(357,358)(371,372)(374,375)(377,
378)(383,384)(386,387)(389,390),(201,202)(208,209)(212,213)(219,220)(229,230)
(251,252)(255,256)(260,261)(264,265)(269,270)(371,372)(374,375)(377,378)(383,
384)(386,387)(389,390),(132,133)(136,137)(140,141)(145,146)(153,154)(158,159)
(166,167)(175,176)(177,178)(181,182)(251,252)(255,256)(260,261)(264,265)(269,
270)(323,324)(328,329)(333,334)(339,340)(343,344)(347,348)(349,350)(355,356)
(357,358)(383,384)(386,387)(389,390),(84,85)(88,89)(101,102)(175,176)(177,178)
(181,182)(208,209)(212,213)(219,220)(229,230)(255,256)(260,261)(264,265)(269,
270)(304,305)(308,309)(311,312)(349,350)(355,356)(357,358)(374,375)(377,378)
(386,387)(389,390)]);
ALF("Co2N2","Co2",[1,2,3,3,3,3,3,2,4,4,3,7,4,10,3,4,9,7,3,10,4,11,4,3,2,4,
12,12,4,10,11,8,10,4,12,11,4,3,11,9,11,3,2,4,4,4,10,3,4,4,2,9,8,12,9,8,12,
11,9,7,3,12,9,8,4,12,9,7,10,11,9,11,26,10,9,8,12,3,4,9,11,25,12,3,2,4,4,3,
4,12,11,12,11,12,11,12,9,10,4,11,11,12,27,4,10,11,12,11,11,12,9,12,28,11,
8,12,11,11,9,3,7,12,11,4,10,12,12,11,13,23,25,2,4,8,8,4,3,9,9,8,9,4,12,12,
8,9,4,12,8,11,12,23,2,3,4,4,12,8,9,4,12,10,4,12,12,8,9,10,12,12,10,4,12,
13,12,9,8,12,27,24,8,9,12,13,13,12,10,27,24,13,26,8,11,23,23,12,23,12,13,
26,8,9,12,13,13,26,4,8,9,12,12,8,9,12,12,10,12,26,2,3,4,12,4,12,12,4,12,
10,8,9,12,12,10,23,13,4,10,12,13,23,26,12,13,12,13,12,10,13,26,13,11,12,
28,11,3,4,11,9,11,7,10,11,9,9,8,12,10,12,9,8,12,4,12,23,13,25,11,12,26,25,
11,9,11,25,13,23,27,28,4,3,9,11,4,8,9,12,9,11,12,12,12,11,27,12,11,27,10,
8,9,12,10,7,9,11,26,25,28,13,25,11,23,28,4,2,8,8,4,9,8,12,8,12,9,12,27,12,
11,4,8,9,12,9,4,3,9,24,8,12,9,8,12,4,12,23,9,12,12,8,27,24,12,23,27,24,23,
11,24,8,23,27,27,24,23,11,12,27,12,8,24,24,28,49,26,25,27,12,9,27,11,12,
27,28,27,48],[
"fusion map determined using the groups"
]);

MOT("3^(1+4)_+:(S3xQD16)",
[
"Sylow 3 normalizer in the sporadic simple Conway group Co2,\n",
"origin: Dixon's Algorithm"
],
[23328,648,288,288,288,72,11664,1296,972,648,324,162,144,24,24,16,324,144,144,
108,108,108,108,72,36,36,36,36,36,18,48,48,48,48,54,72,72,36,12,12,18,24,24,24
,24],
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,13,13,35,18,19,24,18,19,35,36,36,37,37],[1,2,3,4,5,6,1,1,1,1,1,1,13,14,15,16,
2,3,3,2,2,2,2,3,2,6,6,4,5,6,31,32,33,34,7,13,13,13,14,15,17,31,32,33,34]],
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1,1,1,1,1,1,1],[1,-1,1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1
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[TENSOR,[2,5]],
[TENSOR,[3,5]],
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0,0,0,0,0,0,2,2,-1,2,-1,-1,0,1,1,0,0,-1,-1],
[TENSOR,[9,3]],
[TENSOR,[9,2]],
[TENSOR,[9,4]],[2,0,2,-2,-2,0,2,2,2,2,2,2,-2,0,0,2,0,2,2,0,0,0,0,2,0,0,0,-2,
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[TENSOR,[13,2]],[2,0,-2,-2,2,0,2,2,2,2,2,2,0,0,0,0,0,-2,-2,0,0,0,0,-2,0,0,0,
-2,2,0,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,2,0,0,0,0,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[15,3]],
[TENSOR,[15,4]],
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[TENSOR,[20,3]],[8,-2,0,8,0,-2,8,8,8,8,-1,-1,0,0,0,0,-2,0,0,-2,-2,-2,-2,0,1,
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[TENSOR,[22,5]],
[TENSOR,[22,2]],
[TENSOR,[22,6]],[16,-4,0,0,0,0,16,-8,16,-8,-2,-2,0,0,0,0,-4,0,0,-4,2,2,2,0,2,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1,0,0,0,0],
[TENSOR,[26,2]],[18,-6,2,0,0,0,-9,-6,0,3,0,0,2,-2,0,0,3,-1,2,0,-3,0,3,-1,0,0,
0,0,0,0,2,2,0,0,0,-1,2,-1,1,0,0,-1,-1,0,0],
[TENSOR,[28,3]],
[TENSOR,[28,2]],
[TENSOR,[28,4]],[24,-6,0,0,8,-2,24,0,-3,0,6,-3,0,0,0,0,-6,0,0,3,0,0,0,0,0,1,
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[TENSOR,[32,5]],
[TENSOR,[32,2]],
[TENSOR,[32,6]],[36,12,4,0,0,0,-18,6,0,-3,0,0,4,0,0,0,-6,-2,-2,0,-3,0,3,1,0,0
,0,0,0,0,0,0,0,0,0,-2,-2,1,0,0,0,0,0,0,0],
[TENSOR,[36,2]],[36,0,4,0,0,0,-18,-12,0,6,0,0,-4,0,0,0,0,-2,4,0,0,0,0,-2,0,0,
0,0,0,0,0,0,0,0,0,2,-4,2,0,0,0,0,0,0,0],[36,0,4,0,0,0,-18,6,0,-3,0,0,-4,0,0,0,
0,-2,-2,0,-3,6,-3,1,0,0,0,0,0,0,0,0,0,0,0,2,2,-1,0,0,0,0,0,0,0],
[TENSOR,[39,2]],[36,0,-4,0,0,0,-18,-12,0,6,0,0,0,0,0,0,0,2,-4,0,0,0,0,2,0,0,0
,0,0,0,-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0,0,E(8)+E(8)^3,
-E(8)-E(8)^3,0,0],
[TENSOR,[41,2]],[48,0,0,0,0,-4,48,0,-6,0,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0
,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[43,5]],[72,0,-8,0,0,0,-36,12,0,-6,0,0,0,0,0,0,0,4,4,0,0,0,0,-2,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(31,32)(33,34)(42,43)(44,45)]);
ALF("3^(1+4)_+:(S3xQD16)","Co2",[1,2,3,4,4,4,5,5,6,6,6,6,9,11,11,11,17,16,16,
19,19,17,18,20,19,21,21,21,21,21,24,24,24,24,29,35,35,37,40,40,50,56,56,56,
56]);
ALF("3^(1+4)_+:(S3xQD16)","U4(3).D8",[1,39,2,16,16,40,3,3,4,4,4,5,17,54,
54,7,43,9,9,45,45,43,44,10,45,46,46,20,20,47,30,30,30,30,13,24,24,25,60,
60,52,36,36,36,36],[
"fusion map is unique"
]);
ALN("3^(1+4)_+:(S3xQD16)",["Co2N3","U4(3).D8N3"]);

MOT("Co2N7",
[
"structure is (7:3xD8).2,\n",
"origin: Dixon's Algorithm"
],
[336,336,84,12,48,48,168,48,48,12,12,12,12,56,24,24,24,24,56,28,28,24,24,24,24
,28],
[,[1,1,1,1,6,5,2,6,5,5,6,6,5,14,7,7,9,8,14,14,14,17,17,18,18,19],[1,2,3,4,1,1,
7,2,2,3,3,4,4,14,16,15,7,7,19,21,20,16,15,16,15,26],,,,[1,2,3,4,5,6,7,8,9,10,
11,12,13,1,15,16,17,18,2,3,3,22,23,24,25,7]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,1,1,1,1,-1,
-1,1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1],[1,1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1
,1,1,1,1,-1,-1,1,1,1,1,1],
[TENSOR,[2,3]],[1,1,1,1,E(3),E(3)^2,1,E(3),E(3)^2,E(3)^2,E(3),E(3),E(3)^2,1,1
,1,E(3),E(3)^2,1,1,1,E(3)^2,E(3)^2,E(3),E(3),1],
[TENSOR,[5,5]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[3,5]],
[TENSOR,[3,6]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],[2,2,0,0,2,2,-2,2,2,0,0,0,0,2,0,0,-2,-2,2,0,0,0,0,0,0,-2],[2,
-2,0,0,2*E(3)^2,2*E(3),0,-2*E(3)^2,-2*E(3),0,0,0,0,2,E(8)-E(8)^3,-E(8)+E(8)^3,
0,0,-2,0,0,E(24)^11-E(24)^17,-E(24)^11+E(24)^17,-E(24)+E(24)^19,E(24)-E(24)^19
,0],
[TENSOR,[14,2]],
[TENSOR,[14,6]],
[TENSOR,[14,8]],
[TENSOR,[14,5]],
[TENSOR,[14,7]],
[TENSOR,[13,6]],
[TENSOR,[13,5]],[6,6,-6,0,0,0,6,0,0,0,0,0,0,-1,0,0,0,0,-1,1,1,0,0,0,0,-1],
[TENSOR,[22,2]],[6,6,0,0,0,0,-6,0,0,0,0,0,0,-1,0,0,0,0,-1,
-E(7)-E(7)^2+E(7)^3-E(7)^4+E(7)^5+E(7)^6,
E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6,0,0,0,0,1],
[TENSOR,[24,2]],[12,-12,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,2,0,0,0,0,0,0,0]],
[(20,21),(15,16)(22,23)(24,25),(5,6)(8,9)(10,11)(12,13)(17,18)(22,24)(23,
25)]);
ALF("Co2N7","7:6",[1,1,1,5,4,6,1,4,6,6,4,7,3,2,5,5,4,6,2,2,2,3,3,7,7,2]);
ALF("Co2N7","Co2",[1,2,3,4,6,6,7,19,19,20,20,21,21,22,23,23,36,36,42,43,
44,55,55,55,55,57],[
"fusion map is unique up to table automorphisms"
]);

MOT("Co1N5",
[
"origin: Dixon's Algorithm,\n",
"the table is equivalent to that given in Ostermann's book"
],
[10000,2500,500,100,500,250,250,25,80,20,16,16,80,20,80,20,80,20,100,50,50,400
,100,20,80,80,20,16,80,20,80,20,16,80,20,20,80],
[,[1,2,3,4,5,6,7,8,1,4,9,9,9,10,9,10,1,3,5,6,7,1,2,19,22,22,23,17,17,18,17,18,
17,22,23,19,22],,,[1,1,1,1,1,1,1,1,9,9,11,12,13,13,15,15,17,17,22,22,22,22,22,
25,25,26,26,28,29,29,31,31,33,34,34,37,37]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,-1,-1,E(4),-E(4),E(4),E(4),-E(4),-E(4),-1,-1,
1,1,1,1,1,1,1,-1,-1,E(4),-E(4),-E(4),E(4),E(4),-E(4),-1,-1,1,1],
[TENSOR,[2,5]],[1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,E(4),
E(4),E(4),E(4),-E(4),-E(4),-E(4),E(4),E(4),E(4),-E(4),-E(4),-E(4),-E(4)],
[TENSOR,[3,7]],
[TENSOR,[5,7]],
[GALOIS,[9,3]],
[TENSOR,[2,7]],
[TENSOR,[2,8]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],
[TENSOR,[3,5]],
[TENSOR,[2,15]],[4,4,4,4,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,4,4,-1,4,0,
0,0,0,0,0,0,0,0,0,-1,4],
[TENSOR,[17,3]],
[TENSOR,[17,7]],
[TENSOR,[17,8]],[4,4,4,-1,4,4,4,-1,4,-1,0,0,-4,1,-4,1,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,2]],
[TENSOR,[21,5]],
[TENSOR,[21,6]],[16,16,16,-4,-4,-4,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0],[20,20,-5,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-1,0,0,0,0,0,0,0,0
,0,0,4,-1,4,-1,0,0,0,0,0],
[TENSOR,[26,2]],
[TENSOR,[26,5]],
[TENSOR,[26,6]],[20,-5,0,0,0,-5,5,0,0,0,0,0,0,0,0,0,0,0,4,-1,-1,4,-1,0,0,4,-1
,0,0,0,0,0,0,4,-1,0,0],
[TENSOR,[30,3]],
[TENSOR,[30,8]],
[TENSOR,[30,7]],[40,-10,0,0,-10,5,0,0,0,0,0,0,0,0,0,0,0,0,-2,3,-2,8,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[34,7]],[40,-10,0,0,10,0,-5,0,0,0,0,0,0,0,0,0,0,0,-2,-2,3,8,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[36,7]]],
[(11,12)(13,15)(14,16)(24,36)(25,37)(26,34)(27,35)(28,33)(29,31)(30,32)]);
ALF("Co1N5","Co1",[1,17,16,16,17,15,16,17,4,43,14,14,14,72,14,72,4,43,42,
38,41,2,42,73,11,11,73,14,14,72,14,72,14,11,73,73,11],[
"fusion map is unique"
]);
ALF("Co1N5","5^(1+2):GL2(5)",[1,2,3,3,11,12,13,14,8,19,29,30,27,33,28,34,
8,19,16,17,18,4,5,24,6,10,25,30,27,33,28,34,29,10,25,23,7]);

MOT("F3+N5",
[
"Sylow 5 normalizer in the sporadic simple group F3+,\n",
"structure (A4x5^2:4A4).2,\n",
"origin: Dixon's Algorithm,\n",
"constructed independently by A. Hulpke (directly from the group F3+)\n",
"and Thomas Breuer (using the Atlas' structure information)"
],
[28800,9600,3600,1200,400,150,1152,384,144,1152,1152,384,384,144,144,960,320,
192,64,240,80,120,24,30,144,144,48,48,144,144,48,48,36,36,36,36,36,36,36,36,
160,160,160,160,32,32,32,32,16,16,16,16,40,40,40,40],
[,[1,1,3,4,4,6,1,1,3,7,7,7,7,9,9,1,1,7,7,4,4,3,9,6,25,25,25,25,26,26,26,26,33,
34,33,34,35,35,36,36,16,16,17,17,16,16,17,17,10,11,12,13,20,20,21,21],[1,2,1,4
,5,4,7,8,7,11,10,13,12,11,10,16,17,18,19,20,21,16,18,20,1,7,2,8,10,11,12,13,1,
1,7,7,10,11,11,10,42,41,44,43,46,45,48,47,50,49,52,51,54,53,56,55],,[1,2,3,1,2
,3,7,8,9,10,11,12,13,14,15,16,17,18,19,16,17,22,23,22,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,41,42,43,44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[4,2]],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,-1,1
,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,E(4),-E(4),E(4),-E(4),E(4),-E(4),E(4),
-E(4),-E(4),E(4),-E(4),E(4),E(4),-E(4),E(4),-E(4)],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[4,6]],
[TENSOR,[4,7]],[2,2,2,2,2,2,-2,-2,-2,-2*E(4),2*E(4),-2*E(4),2*E(4),-2*E(4),
2*E(4),0,0,0,0,0,0,0,0,0,-1,1,-1,1,-E(4),E(4),-E(4),E(4),-1,-1,1,1,-E(4),E(4),
E(4),-E(4),1-E(4),1+E(4),1-E(4),1+E(4),-1+E(4),-1-E(4),-1+E(4),-1-E(4),0,0,0,0
,1-E(4),1+E(4),1-E(4),1+E(4)],
[TENSOR,[11,6]],
[TENSOR,[11,2]],
[TENSOR,[11,7]],[4,4,4,4,4,4,-4,-4,-4,-4*E(4),4*E(4),-4*E(4),4*E(4),-4*E(4),
4*E(4),0,0,0,0,0,0,0,0,0,1,-1,1,-1,E(4),-E(4),E(4),-E(4),1,1,-1,-1,E(4),-E(4),
-E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,6]],[24,24,24,-1,-1,-1,0,0,0,0,0,0,0,0,0,4,4,0,0,-1,-1,4,0,-1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,0,0,0,0,0,0,0,0,1,1,1,1],
[TENSOR,[17,2]],
[TENSOR,[17,6]],
[TENSOR,[17,7]],[2,2,-1,2,2,-1,2,2,-1,-2,-2,-2,-2,1,1,-2,-2,2,2,-2,-2,1,-1,1,
2,2,2,2,-2,-2,-2,-2,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,6]],[2,2,-1,2,2,-1,2,2,-1,-2,-2,-2,-2,1,1,-2,-2,2,2,-2,-2,1,-1,1,
-1,-1,-1,-1,1,1,1,1,-1,2,-1,2,1,1,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,
-1,2,2,-1,2,2,-1,-2,-2,-2,-2,1,1,-2,-2,2,2,-2,-2,1,-1,1,-1,-1,-1,-1,1,1,1,1,2,
-1,2,-1,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[23,6]],
[TENSOR,[24,6]],[6,6,-3,6,6,-3,6,6,-3,6,6,6,6,-3,-3,-2,-2,-2,-2,-2,-2,1,1,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,6]],[4,4,-2,4,4,-2,-4,-4,2,-4*E(4),4*E(4),-4*E(4),4*E(4),2*E(4),
-2*E(4),0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2*E(4),2*E(4),-2*E(4),2*E(4),1,1,-1,-1,
E(4),-E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,6]],[4,4,-2,4,4,-2,-4,-4,2,-4*E(4),4*E(4),-4*E(4),4*E(4),2*E(4),
-2*E(4),0,0,0,0,0,0,0,0,0,1,-1,1,-1,E(4),-E(4),E(4),-E(4),-2,1,2,-1,-2*E(4),
2*E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[31,6]],[4,4,-2,4,4,-2,-4,-4,2,-4*E(4),4*E(4),-4*E(4),4*E(4),2*E(4),
-2*E(4),0,0,0,0,0,0,0,0,0,1,-1,1,-1,E(4),-E(4),E(4),-E(4),1,-2,-1,2,E(4),-E(4)
,2*E(4),-2*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,6]],[48,48,-24,-2,-2,1,0,0,0,0,0,0,0,0,0,-8,-8,0,0,2,2,4,0,-1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[35,6]],[3,-1,0,3,-1,0,3,-1,0,3,3,-1,-1,0,0,3,-1,3,-1,3,-1,0,0,0,3,3,
-1,-1,3,3,-1,-1,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1],
[TENSOR,[37,2]],
[TENSOR,[37,6]],
[TENSOR,[37,7]],[6,-2,0,6,-2,0,6,-2,0,-6,-6,2,2,0,0,-6,2,6,-2,-6,2,0,0,0,-3,
-3,1,1,3,3,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[41,6]],[6,-2,0,6,-2,0,-6,2,0,-6*E(4),6*E(4),2*E(4),-2*E(4),0,0,0,0,0
,0,0,0,0,0,0,-3,3,1,-1,-3*E(4),3*E(4),E(4),-E(4),0,0,0,0,0,0,0,0,1-E(4),1+E(4)
,-1+E(4),-1-E(4),-1+E(4),-1-E(4),1-E(4),1+E(4),0,0,0,0,1-E(4),1+E(4),-1+E(4),
-1-E(4)],
[TENSOR,[43,6]],
[TENSOR,[43,2]],
[TENSOR,[43,7]],[9,-3,0,9,-3,0,9,-3,0,9,9,-3,-3,0,0,-3,1,-3,1,-3,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1],
[TENSOR,[47,2]],
[TENSOR,[47,6]],
[TENSOR,[47,7]],[12,-4,0,12,-4,0,-12,4,0,-12*E(4),12*E(4),4*E(4),-4*E(4),0,0,
0,0,0,0,0,0,0,0,0,3,-3,-1,1,3*E(4),-3*E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[51,6]],[72,-24,0,-3,1,0,0,0,0,0,0,0,0,0,0,12,-4,0,0,-3,1,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,4,4,0,0,0,0,0,0,0,0,1,1,-1,-1],
[TENSOR,[53,2]],
[TENSOR,[53,6]],
[TENSOR,[53,7]]],
[(33,34)(35,36)(37,40)(38,39),
(10,11)(12,13)(14,15)(29,30)(31,32)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)
(49,50)(51,52)(53,54)(55,56)
]);
ALF("F3+N5","(A4xO8+(2).3).2",[1,69,110,12,80,121,4,72,113,11,11,79,79,
120,120,3,71,11,79,23,91,112,120,132,29,32,97,100,37,37,105,105,139,140,
145,146,155,155,156,156,44,44,167,167,48,48,171,171,57,57,180,180,66,66,
189,189],[
"fusion map is unique up to table automorphims"
]);
ALF("F3+N5","Symm(4)",[1,2,3,1,2,3,1,2,3,1,1,2,2,3,3,1,2,1,2,1,2,3,3,3,1,1,2,
2,1,1,2,2,3,3,3,3,3,3,3,3,4,4,5,5,4,4,5,5,4,4,5,5,4,4,5,5]);
ALF("F3+N5","Fi22N5",[1,1,1,12,12,12,2,2,2,5,6,5,6,5,6,3,3,11,11,16,16,3,
11,16,4,13,4,13,18,17,18,17,4,4,13,13,18,17,17,18,7,8,7,8,9,10,9,10,15,14,
15,14,19,20,19,20]);
ALF("F3+N5","S4x5^2:4S4",[1,21,41,12,32,52,2,22,42,5,6,25,26,45,46,3,23,
11,31,16,36,43,51,56,4,13,24,33,18,17,38,37,44,44,53,53,58,57,57,58,67,68,
87,88,69,70,89,90,75,74,95,94,79,80,99,100],[
"fusion map is unique"
]);
ALF("F3+N5","F3+",[1,2,4,12,35,54,3,3,16,9,9,11,11,40,40,2,3,9,11,35,36,
13,40,90,7,22,19,20,43,43,50,50,8,8,23,23,46,46,47,47,10,10,9,9,10,10,11,
11,26,26,28,28,67,67,68,68],[
"fusion map determined up to table automorphisms\n",
"by factorization through (A4xO8+(2).3).2"
]);

MOT("S4x5^2:4S4",
[
"Sylow 5 normalizer in F3+.2"
],
0,
0,
0,
[(  5,  6)(  7,  8)(  9, 10)( 14, 15)( 17, 18)( 19, 20)( 25, 26)( 27, 28)
( 29, 30)( 34, 35)( 37, 38)( 39, 40)( 45, 46)( 47, 48)( 49, 50)( 54, 55)
( 57, 58)( 59, 60)( 65, 66)( 67, 68)( 69, 70)( 74, 75)( 77, 78)( 79, 80)
( 85, 86)( 87, 88)( 89, 90)( 94, 95)( 97, 98)( 99,100)],
["ConstructDirectProduct",[["s4"],["Fi22N5"]]]);
ALF("S4x5^2:4S4","F3+.2",[1,3,2,7,9,9,100,100,101,101,9,12,22,115,115,35,
43,43,148,148,2,3,3,19,11,11,101,101,101,101,11,35,20,116,116,36,49,49,
149,149,4,16,13,8,40,40,120,120,125,125,40,53,23,153,153,83,46,46,177,177,
98,99,99,110,102,102,10,10,10,10,102,118,113,26,26,119,133,133,65,65,100,
101,101,128,103,103,9,9,11,11,103,148,129,28,28,149,132,132,66,66],[
"fusion map is unique"
]);
ALN("S4x5^2:4S4",["F3+.2N5"]);

MOT("BN7",
[
"Sylow 7 normalizer in the sporadic simple group B,\n",
"structure (2^2x7^2:(3x2A4)).2,\n",
"origin: Dixon's Algorithm,\n",
"constructed by Thomas Breuer using the Atlas' structure information"
],
[28224,28224,14112,588,588,588,588,576,576,576,576,288,288,288,576,576,576,576
,576,576,288,288,96,96,48,96,96,96,96,48,48,504,504,72,504,504,504,504,504,504
,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,84,84,84,84,84,84,84,84,24,24,48
,48,48,48,24,24,24,24,48,48,48,48,48,48,48,48],
[,[1,1,1,4,4,4,4,9,8,9,8,9,8,1,1,1,9,8,9,8,9,8,15,15,15,18,17,18,17,18,17,33,
32,34,33,32,33,32,33,32,34,34,34,33,32,34,34,34,34,33,32,33,32,33,32,57,56,57,
56,57,56,57,56,15,16,23,23,24,24,18,17,20,19,27,27,26,26,29,29,28,28],[1,2,3,4
,5,6,7,1,1,2,2,3,3,14,15,16,15,15,16,16,14,14,23,24,25,23,23,24,24,25,25,1,1,1
,3,3,3,3,2,2,15,2,16,15,15,3,3,14,14,14,14,14,14,16,16,4,4,6,6,7,7,5,5,64,65,
67,66,69,68,64,64,65,65,66,67,67,66,68,69,69,68],,,,[1,2,3,1,2,3,3,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,32,33,35,36,37,38,39,40,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81]],
0,
[(66,67)(68,69)(74,75)(76,77)(78,79)(80,81),
( 6, 7)(35,37)(36,38)(46,47)(48,49)(50,52)(51,53)(58,60)(59,61),
( 8, 9)(10,11)(12,13)(17,18)(19,20)(21,22)(26,27)(28,29)(30,31)(32,33)(35,36)
(37,38)(39,40)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)
(62,63)(66,67)(68,69)(70,71)(72,73)(74,76)(75,77)(78,80)(79,81)
],
["ConstructIndexTwoSubdirectProduct","V4","D8","7^2:(3x2A4)","7^2:(3x2S4)",
[73,74,75,76,77,78,79,80,81,127,128,129,130,131,132,133,134,135],(2,4,8,23,16,
44,21,11,33,55,49,38,6,18,56,51,37,3,9,27,29,40,13,34,54,48,36,62,58,50,35,63,
60,59,52,46,31,42,14,41,12,32,43,22,10,26,24,20,5,15,45,25,19)(7,17,57,53,47,
30,39)(64,65,68,72,78,76,71,79,77,70,81,74,66,69,80,75,67,73),(1,14,19,18,8,2,
12,21,17,7)(3,10,23,5,11,22,15,20,16,6,9)(4,13,24)(25,26,27)(28,36,34,29,31,
35)(30,33,32)(37,50,43,38,41,40,51,44)(39,42)(45,49,47,48)(52,53,54)(55,58,59,
63,60,57,62,61)(64,68,71,69,65,66,72,70)(73,75)(76,78)(77,79,80,81)]);
ALF("BN7","D8",[1,2,4,1,2,4,4,1,1,2,2,4,4,4,1,2,1,1,2,2,4,4,1,2,4,1,1,2,2,
4,4,1,1,1,4,4,4,4,2,2,1,2,2,1,1,4,4,4,4,4,4,4,4,2,2,1,1,4,4,4,4,2,2,5,3,5,
5,3,3,5,5,3,3,5,5,5,5,3,3,3,3]);
ALF("BN7","7^2:(3x2S4)",[1,1,1,2,2,2,2,3,4,3,4,3,4,5,5,5,6,7,6,7,6,7,8,8,
8,9,10,9,10,9,10,11,12,13,11,12,11,12,11,12,14,13,14,15,16,13,13,14,14,15,
16,15,16,15,16,17,18,17,18,17,18,17,18,19,19,20,21,20,21,22,23,22,23,25,
24,26,27,25,24,26,27]);
ALF("BN7","B",[1,4,2,31,78,76,77,7,7,30,30,23,23,5,5,4,28,28,30,30,29,29,
17,15,17,72,72,71,71,72,72,6,6,7,21,21,20,20,25,25,28,30,30,27,27,23,23,
29,29,24,24,27,27,25,25,109,109,166,166,167,167,168,168,17,16,45,45,42,42,
72,72,74,74,127,127,127,127,125,125,125,125],[
"determined by factorization of ThN7 -> Th -> B through BN7"
]);

MOT("11^2:(5x2.A5)",
[
"origin: Dixon's Algorithm,\n",
"Sylow 11 normalizer in the Monster, maximal subgroup of M,\n",
"the structure is 11^2:(5x2.A5),\n",
"and there is a unique class of 5x2.A5 subgroups in GL(2,11)"
],
[72600,605,600,600,600,600,600,600,600,600,600,50,50,50,50,550,55,50,50,50,50,
550,55,50,50,550,55,50,50,50,50,550,55,50,50,20,20,20,20,20,30,30,30,30,30,30,
30,30,30,30],
[,[1,2,1,6,6,8,8,11,11,5,5,25,25,30,30,32,33,32,34,34,26,26,27,12,12,16,17,16,
19,19,22,22,23,15,15,4,10,3,9,7,42,42,46,46,48,48,49,49,43,43],[1,2,3,10,11,5,
4,6,7,9,8,25,24,35,34,26,27,28,30,29,31,32,33,13,12,22,23,21,14,15,18,16,17,19
,20,37,39,38,40,36,3,1,11,10,4,5,7,6,8,9],,[1,2,3,3,1,1,3,1,3,3,1,1,3,3,1,1,2,
3,1,3,3,1,2,3,1,1,2,3,3,1,3,1,2,1,3,38,38,38,38,38,41,42,42,41,41,42,41,42,42,
41],,,,,,[1,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,18,19,20,21,22,22,24,25,26
,26,28,29,30,31,32,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,E(5)^4,E(5)^4,E(5)^3,E(5)^3,E(5),E(5),E(5)^2,
E(5)^2,1,1,E(5)^4,E(5)^4,E(5)^3,E(5)^3,E(5)^3,E(5),E(5),E(5)^2,E(5)^2,E(5)^2,1
,1,E(5)^4,E(5)^4,E(5)^4,E(5)^3,E(5)^3,E(5),E(5),E(5),E(5)^2,E(5)^2,E(5)^2,E(5)
,1,E(5)^3,E(5)^4,1,1,E(5)^4,E(5)^4,E(5)^3,E(5)^3,E(5),E(5),E(5)^2,E(5)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[2,2,-2,-2,2,2,-2,2,-2,-2,2,E(5)+E(5)^4,-E(5)-E(5)^4,
-E(5)-E(5)^4,E(5)+E(5)^4,E(5)+E(5)^4,E(5)+E(5)^4,-E(5)-E(5)^4,E(5)+E(5)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,E(5)+E(5)^4,E(5)+E(5)^4,-E(5)^2-E(5)^3,E(5)^2+E(5)^3
,E(5)^2+E(5)^3,E(5)^2+E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,E(5)^2+E(5)^3,
-E(5)^2-E(5)^3,E(5)^2+E(5)^3,E(5)^2+E(5)^3,E(5)^2+E(5)^3,-E(5)^2-E(5)^3,0,0,0,
0,0,1,-1,-1,1,1,-1,1,-1,-1,1],
[GALOIS,[6,2]],
[TENSOR,[6,2]],
[TENSOR,[6,5]],
[TENSOR,[7,4]],
[TENSOR,[7,3]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],
[TENSOR,[7,2]],
[TENSOR,[7,5]],[3,3,3,3,3,3,3,3,3,3,3,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-1,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[16,2]],
[TENSOR,[16,2]],
[TENSOR,[16,5]],
[TENSOR,[17,4]],
[TENSOR,[17,3]],
[TENSOR,[16,3]],
[TENSOR,[16,4]],
[TENSOR,[17,2]],
[TENSOR,[17,5]],[4,4,-4,-4,4,4,-4,4,-4,-4,4,-1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,
-1,-1,-1,1,1,-1,1,-1,-1,-1,1,0,0,0,0,0,-1,1,1,-1,-1,1,-1,1,1,-1],[4,4,4,4,4,4,
4,4,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1],
[TENSOR,[26,5]],
[TENSOR,[26,4]],
[TENSOR,[26,3]],
[TENSOR,[26,2]],
[TENSOR,[27,2]],
[TENSOR,[27,3]],
[TENSOR,[27,4]],
[TENSOR,[27,5]],[5,5,5,5,5,5,5,5,5,5,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[36,2]],
[TENSOR,[36,3]],
[TENSOR,[36,4]],
[TENSOR,[36,5]],[6,6,-6,-6,6,6,-6,6,-6,-6,6,1,-1,-1,1,1,1,-1,1,-1,-1,1,1,-1,1
,1,1,-1,-1,1,-1,1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[41,2]],
[TENSOR,[41,3]],
[TENSOR,[41,4]],
[TENSOR,[41,5]],[120,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,10,-1,0,0,0,0,10,-1,0,0,10,
-1,0,0,0,0,10,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[46,5]],
[TENSOR,[46,2]],
[TENSOR,[46,3]],
[TENSOR,[46,4]]],
[(4,9)(5,8)(6,11)(7,10)(14,20)(15,19)(16,22)(17,23)(18,21)(26,32)(27,33)(28,
31)(29,35)(30,34)(36,39)(37,40)(43,48)(44,47)(45,50)(46,49),(4,10,9,7)(5,11,8,
6)(12,25)(13,24)(14,35,20,29)(15,34,19,30)(16,26,22,32)(17,27,23,33)(18,28,21,
31)(36,37,39,40)(43,49,48,46)(44,50,47,45)]);
ALF("11^2:(5x2.A5)","M",[1,34,3,32,12,12,32,12,32,32,12,12,32,33,12,11,
147,30,12,33,30,11,147,32,12,11,147,30,33,12,30,11,147,12,33,68,68,10,68,
68,18,6,53,102,102,53,102,53,53,102],[
"fusion determined uniquely by the fact that the group contains 30E and\n",
"10E elements"
]);
ALN("11^2:(5x2.A5)",["11^2:(5x2A5)","MN11"]);

MOT("13^(1+2):(3x4S4)",
[
"Sylow 13 normalizer in the sporadic simple group M,\n",
"structure: 13^{1+2}_+:(3x4S4),\n",
"origin: Dixon's Algorithm,\n",
"constructed by Thomas Breuer using the Atlas' structure information"
],
[632736,52728,676,507,3744,312,288,288,288,288,288,288,288,288,288,288,624,624
,48,48,48,48,52,52,468,468,468,468,36,36,36,36,36,36,36,36,78,78,39,39,78,78,
624,624,48,48,24,24,48,48,48,48,48,48,48,48,24,24,24,24,52,52],
[,[1,2,3,4,1,2,5,5,10,9,10,9,12,11,12,11,1,5,9,10,12,11,3,6,25,27,26,25,27,26,
29,30,29,30,28,28,37,38,40,39,37,38,17,17,17,17,7,8,19,20,19,20,19,20,19,20,14
,13,15,16,23,23],[1,2,3,4,5,6,8,7,1,1,5,5,8,8,7,7,17,18,17,17,18,18,23,24,1,1,
1,5,5,5,8,8,7,7,8,7,2,2,4,4,6,6,44,43,46,45,48,47,46,46,45,45,44,44,43,43,48,
48,47,47,62,61],,,,,,,,,,[1,1,1,1,5,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,17,18,25,26,27,28,29,30,31,32,33,34,35,36,25,25,26,27,28,28,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,43,44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1
,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,1,1,1,1,-1,-1],
[TENSOR,[4,2]],[1,1,1,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,1,1,E(3)^2,E(3),E(3),E(3)^2,1,1,1,E(3),E(3)^2,1,E(3),E(3)^2,E(3)^2,E(3)
,E(3)^2,E(3),1,1,1,1,E(3),E(3)^2,1,1,1,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),1,1],
[TENSOR,[6,6]],
[TENSOR,[2,6]],
[TENSOR,[2,7]],
[TENSOR,[3,7]],
[TENSOR,[3,6]],
[TENSOR,[4,7]],
[TENSOR,[4,6]],
[TENSOR,[4,9]],
[TENSOR,[4,8]],[1,1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,1,1,1
,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-E(4),E(4),-E(4),E(4),E(4),-E(4),-E(4),
-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),E(4),E(4),-E(4),-E(4),-E(4),E(4)],
[TENSOR,[2,16]],
[TENSOR,[6,16]],
[TENSOR,[6,18]],
[TENSOR,[2,18]],
[TENSOR,[2,19]],
[TENSOR,[3,16]],
[TENSOR,[3,19]],
[TENSOR,[3,18]],
[TENSOR,[4,19]],
[TENSOR,[4,18]],
[TENSOR,[4,21]],
[TENSOR,[4,20]],
[TENSOR,[4,16]],
[TENSOR,[4,17]],[2,2,2,2,-2,-2,-2*E(4),2*E(4),2*E(3)^2,2*E(3),-2*E(3)^2,
-2*E(3),-2*E(12)^11,-2*E(12)^7,2*E(12)^11,2*E(12)^7,0,0,0,0,0,0,0,0,-1,-E(3)^2
,-E(3),1,E(3)^2,E(3),E(12)^7,E(12)^11,-E(12)^7,-E(12)^11,E(4),-E(4),-1,-1,
-E(3)^2,-E(3),1,1,-1+E(4),-1-E(4),1-E(4),1+E(4),0,0,E(12)^8-E(12)^11,
E(12)^4-E(12)^7,E(12)^8+E(12)^11,E(12)^4+E(12)^7,-E(12)^8+E(12)^11,
-E(12)^4+E(12)^7,-E(12)^8-E(12)^11,-E(12)^4-E(12)^7,0,0,0,0,-1+E(4),-1-E(4)],
[TENSOR,[31,7]],
[TENSOR,[31,17]],
[TENSOR,[31,21]],
[TENSOR,[31,6]],
[TENSOR,[31,20]],
[TENSOR,[31,2]],
[TENSOR,[31,9]],
[TENSOR,[31,16]],
[TENSOR,[31,19]],
[TENSOR,[31,8]],
[TENSOR,[31,18]],[4,4,4,4,-4,-4,-4*E(4),4*E(4),4,4,-4,-4,-4*E(4),-4*E(4),
4*E(4),4*E(4),0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-E(4),-E(4),E(4),E(4),-E(4),E(4),
1,1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[43,16]],
[TENSOR,[43,7]],
[TENSOR,[43,19]],
[TENSOR,[43,6]],
[TENSOR,[43,18]],[72,72,7,-6,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1],
[TENSOR,[49,2]],
[TENSOR,[49,16]],
[TENSOR,[49,17]],[96,96,-8,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,12,
0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[53,6]],
[TENSOR,[53,7]],[156,-13,0,0,12,-1,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,0,0,0,1,12,0
,0,12,0,0,0,0,0,0,0,0,-1,-1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
,[156,-13,0,0,12,-1,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,0,0,0,1,-6,0,0,-6,0,0,0,0,0,
0,0,0,
E(39)^7+E(39)^14+E(39)^17+E(39)^19+E(39)^23+E(39)^28+E(39)^29+E(39)^31
 +E(39)^34+E(39)^35+E(39)^37+E(39)^38
,
E(39)+E(39)^2+E(39)^4+E(39)^5+E(39)^8+E(39)^10+E(39)^11+E(39)^16+E(39)^20
 +E(39)^22+E(39)^25+E(39)^32
,0,0,
E(39)^7+E(39)^14+E(39)^17+E(39)^19+E(39)^23+E(39)^28+E(39)^29+E(39)^31
 +E(39)^34+E(39)^35+E(39)^37+E(39)^38
,
E(39)+E(39)^2+E(39)^4+E(39)^5+E(39)^8+E(39)^10+E(39)^11+E(39)^16+E(39)^20
 +E(39)^22+E(39)^25+E(39)^32
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[57,7]],[312,-26,0,0,-24,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,0,
0,12,0,0,0,0,0,0,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
312,-26,0,0,-24,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,-6,0,0,0,0,0,0,0,0
,
-E(39)-E(39)^2-E(39)^4-E(39)^5-E(39)^8-E(39)^10-E(39)^11-E(39)^16-E(39)^20
 -E(39)^22-E(39)^25-E(39)^32
,
-E(39)^7-E(39)^14-E(39)^17-E(39)^19-E(39)^23-E(39)^28-E(39)^29-E(39)^31
 -E(39)^34-E(39)^35-E(39)^37-E(39)^38
,0,0,
E(39)+E(39)^2+E(39)^4+E(39)^5+E(39)^8+E(39)^10+E(39)^11+E(39)^16+E(39)^20
 +E(39)^22+E(39)^25+E(39)^32
,
E(39)^7+E(39)^14+E(39)^17+E(39)^19+E(39)^23+E(39)^28+E(39)^29+E(39)^31
 +E(39)^34+E(39)^35+E(39)^37+E(39)^38
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[60,7]],[468,-39,0,0,36,-3,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(37,38)(41,42),
( 9,10)(11,12)(13,14)(15,16)(19,20)(21,22)(26,27)(29,30)(31,32)(33,34)(39,40)
(49,50)(51,52)(53,54)(55,56)(57,58)(59,60),
( 7, 8)(13,15)(14,16)(31,33)(32,34)(35,36)(43,44)(45,46)(47,48)(49,51)(50,52)
(53,55)(54,56)(57,60)(58,59)(61,62)]);
ALF("13^(1+2):(3x4S4)","M",[1,46,46,45,3,90,10,10,6,6,18,18,44,44,44,44,3,
10,18,18,44,44,90,145,5,6,6,14,18,18,44,44,44,44,40,40,121,122,120,120,
172,173,10,10,10,10,26,26,44,44,44,44,44,44,44,44,87,87,87,87,145,145],[
"fusion map is unique up to table automorphisms"
]);
ALN("13^(1+2):(3x4S4)",["MN13","MN13B"]);

MOT("13:4",
[
"9th maximal subgroup of 3D4(2)"
],
0,
0,
0,
[(5,7),(2,3,4)],
["ConstructPermuted",["P:Q",[13,4]]]);
ARC("13:4","tomfusion",rec(name:="13:4",map:=[1,4,4,4,3,2,3],text:=[
"fusion map is unique"
]));
ALF("13:4","13:12",[1,2,2,2,11,8,5],[
"fusion map is unique up to table aut."
]);
ALF("13:4","3D4(2)",[1,21,22,23,8,3,8],[
"fusion map is unique up to table automorphisms"
]);
ALF("13:4","L2(25).2_2",[1,9,11,10,14,2,14],[
"fusion map determined up to table autom. by Brauer tables"
]);
ALF("13:4","Sz(8)",[1,9,10,11,3,2,4],[
"fusion map is unique up to table autom."
]);
ALN("13:4",["3D4(2)N13","Sz(8)N13"]);

MOT("13:12",
[
"3rd maximal subgroup of Sz(8).3,\n",
"constructions: AGL(1,13)"
],
0,
0,
0,
[(3,7)(4,12)(6,10)(9,13),(3,9)(5,11)(7,13)],
["ConstructPermuted",["P:Q",[13,12]]]);
ALF("13:12","Sz(8).3",[1,7,12,11,4,8,13,2,14,9,3,10,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("13:12","2F4(2)'.2",[1,15,24,9,20,4,25,3,24,4,20,9,25],[
"fusion map determined using that the subgroup is not contained in 2F4(2)'"
]);
ALF("13:12","A13.2",[1,38,84,22,60,8,84,4,84,8,60,22,84],[
"fusion map is unique"
]);
ALF("13:12","3D4(2).3",[1,17,40,31,8,24,41,3,40,25,8,30,41],[
"fusion map is unique up to table aut."
]);
ALF("13:12","G2(3).2",[1,17,23,9,19,5,24,2,24,5,19,9,23],[
"fusion map is unique up to table aut."
]);
ALF("13:12","G2(4).2",[1,21,34,12,27,5,34,3,34,5,27,12,34],[
"fusion map is unique"
]);
ALF("13:12","Fi22.2",[1,47,95,25,67,8,95,4,95,8,67,25,95],[
"fusion map determined by factorization through 2F4(2)'.2"
]);
ALF("13:12","Suz.2",[1,30,56,16,41,6,56,3,56,6,41,16,56],[
"determined using that 13:12 is not contained in Suz"
]);
ALF("13:12","F4(2)",[1,71,69,35,22,8,70,5,69,8,22,35,70],[
"fusion map determined up to table aut. by factorization through 2F4(2)'.2"
]);
ALN("13:12",["AGL(1,13)","F4(2)N13"]);

MOT("2^(3+3):7",
[
"origin: Dixon's Algorithm,\n",
"1st maximal subgroup of Sz(8)"
],
[448,64,16,16,7,7,7,7,7,7],
[,[1,1,2,2,7,8,9,10,5,6],,,,,[1,2,4,3,1,1,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1],[1,1,1,1,E(7),E(7)^3,E(7)^2,E(7)^6,E(7)^4,E(7)^5],
[GALOIS,[2,5]],
[GALOIS,[2,4]],
[TENSOR,[2,3]],
[TENSOR,[2,2]],
[TENSOR,[2,6]],[7,7,-1,-1,0,0,0,0,0,0],[14,-2,2*E(4),-2*E(4),0,0,0,0,0,0],
[GALOIS,[9,3]]],
[(3,4),( 5, 6, 7, 8, 9,10)]);
ARC("2^(3+3):7","tomfusion",rec(name:="2^(3+3):7",map:=[1,2,4,4,5,5,5,5,5,
5],text:=[
"fusion map is unique"
]));
ALF("2^(3+3):7","2^(3+3):7:3",[1,2,3,4,5,6,5,6,5,6],[
"fusion map is unique up to table aut."
]);
ALF("2^(3+3):7","Sz(8)",[1,2,3,4,6,8,7,6,8,7],[
"fusion map is unique up to table automorphisms"
]);
ALN("2^(3+3):7",["Sz(8)N2"]);

MOT("2^(3+3):7:3",
[
"origin: Dixon's Algorithm,\n",
"2nd maximal subgroup of Sz(8).3"
],
[1344,192,48,48,7,7,12,12,12,12,12,12,12,12],
[,[1,1,2,2,5,6,8,7,8,7,10,9,10,9],[1,2,4,3,6,5,1,1,2,2,3,3,4,4],,,,[1,2,4,3,1,
1,7,8,9,10,13,14,11,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[3,3,3,3,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0,0
,0],
[GALOIS,[4,3]],[7,7,-1,-1,0,0,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],[14,-2,2*E(4),-2*E(4),0,0,-1,-1,1,1,E(4),E(4),-E(4),-E(4)],
[GALOIS,[9,3]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],
[TENSOR,[9,2]],
[TENSOR,[9,3]]],
[(5,6),( 7, 8)( 9,10)(11,12)(13,14),( 3, 4)(11,13)(12,14)]);
ALF("2^(3+3):7:3","Sz(8).3",[1,2,3,4,6,6,8,9,10,11,14,15,12,13],[
"fusion map is unique up to table automorphisms"
]);
ALN("2^(3+3):7:3",["Sz(8).3N2"]);

MOT("7:6xA5.2",
0,
0,
0,
0,
[(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,36)(23,37)(24,38)(25,39)
(26,40)(27,41)(28,42)],
["ConstructDirectProduct",[["7:6"],["A5.2"]]]);
ALF("7:6xA5.2","Fi23",[1,3,5,13,2,9,14,29,60,76,92,59,88,97,20,26,28,91,
25,55,27,7,24,8,62,18,51,23,4,4,22,40,4,11,22,7,24,8,62,18,51,23,20,26,28,
91,25,55,27],[
"fusion map is unique"
]);
ALF("7:6xA5.2","A12.2",[1,2,5,13,41,44,49,22,34,38,40,69,73,76,50,57,56,
75,19,33,21,6,17,8,36,52,65,54,42,43,51,61,4,11,16,6,17,8,36,52,65,54,50,
57,56,75,19,33,21],[
"fusion map is unique"
]);
ALN("7:6xA5.2",["A12.2N7","Fi23N7"]);

MOT("HNN2",
[
"origin: Dixon's Algorithm,\n",
"Sylow 2 normalizer in the sporadic simple Harada-Norton group HN",
],
[49152,49152,1536,1024,2048,1024,768,1536,24576,12288,768,768,768,768,768,768,
64,384,96,96,512,128,256,512,64,16,32,32,64,64,256,64,256,256,256,64,64,256,64
,256,256,256,192,192,96,48,48,96,96,48,48,48,48,24,48,48,24,24,192,192,96,48,
48,96,96,48,48,48,48,24,48,48,24,24],
[,[1,1,1,2,1,1,2,1,1,1,1,1,2,2,1,1,5,9,8,3,9,5,10,1,4,22,21,24,6,6,9,6,2,10,10
,4,5,10,4,10,9,1,59,59,59,60,59,59,59,59,59,60,60,65,59,59,64,61,43,43,43,44,
43,43,43,43,43,44,44,49,43,43,45,48],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
1,2,3,7,10,8,9,11,12,13,14,18,15,16,19,20,1,2,3,7,10,8,9,11,12,13,14,18,15,16,
20,19]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,
1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,1,1,1,1
,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1
,-1,-1,-1,-1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,-1
,1,1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,1,1
,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,1,
-1,-1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,1,1,E(3)^2,E(3)^2,E(3)^2,E(3)^2,E(3)^2,
E(3)^2,E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,E(3)^2,
E(3)^2,E(3),E(3),E(3),E(3),E(3),E(3),E(3),-E(3),-E(3),-E(3),-E(3),-E(3),-E(3),
-E(3),E(3),E(3)],
[GALOIS,[5,2]],
[TENSOR,[5,4]],
[TENSOR,[6,4]],
[TENSOR,[2,7]],
[TENSOR,[2,8]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[2,2,-2,2,2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,2,-2,2,2,0,0,0,0,0
,0,2,-2,2,2,2,0,0,2,-2,2,2,2,2,2,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,2,2,-2,-2,2,-2
,2,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,6]],
[TENSOR,[13,5]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[16,4]],
[TENSOR,[16,3]],
[TENSOR,[16,2]],[6,6,6,6,6,6,6,6,6,6,-6,-6,-6,-6,0,0,0,0,0,0,-2,-2,-2,-2,2,0,
0,0,-2,-2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,6,6,6,-6,-6,-6,-6,0,0,0,0,0,0,-2,-2,
-2,-2,2,0,0,0,2,2,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,2]],
[TENSOR,[20,2]],[6,6,-6,6,6,6,-6,-6,6,6,0,0,0,0,0,0,0,0,0,0,6,-6,6,6,0,0,0,0,
0,0,-2,2,-2,-2,-2,0,0,-2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[6,6,-6,6,6,6,-6,-6,6,6,0,0,0,0,0,0,0,0,0,0,-2,2,-2,-2,
0,0,0,0,-4,4,2,-2,2,2,2,0,0,-2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,-6,6,6,6,-6,-6,6,6,0,0,0,0,0,0,0,0,0,0,-2,2,
-2,-2,0,0,0,0,0,0,-2,2,-2,-2,-2,-4,4,2,-2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[26,2]],
[TENSOR,[25,2]],[12,12,0,-4,12,-4,0,0,12,12,0,0,0,0,-6,-6,2,-6,0,0,4,0,-4,4,0
,0,-2,2,0,0,0,0,0,0,0,0,0,4,0,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[12,12,0,-4,12,-4,0,0,12,12,0,0,0,0,-6,-6,2,-6,0,0,4,
0,-4,4,0,0,2,-2,0,0,0,0,0,0,0,0,0,-4,0,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,2]],
[TENSOR,[29,2]],[16,16,4,0,0,0,-4,4,16,-16,-4,4,4,-4,-4,-4,0,4,2,-2,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,
1,-1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1],
[TENSOR,[33,4]],
[TENSOR,[33,3]],
[TENSOR,[33,2]],
[TENSOR,[33,11]],
[TENSOR,[33,12]],
[TENSOR,[33,9]],
[TENSOR,[33,10]],
[TENSOR,[33,7]],
[TENSOR,[33,8]],
[TENSOR,[33,5]],
[TENSOR,[33,6]],[24,24,0,-8,24,-8,0,0,24,24,0,0,0,0,0,0,0,0,0,0,-8,0,8,-8,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],[24,24,0,8,-8,-8,0,0,24,24,0,0,0,0,0,0,0,0,0,0,-8,0,0,8,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0],[24,24,0,8,-8,-8,0,0,24,24,0,0,0,0,0,0,0,0,0,0,-8,0,0,8,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0],[24,24,0,8,-8,-8,0,0,24,24,0,0,0,0,0,0,0,0,0,0,8,0,0,
-8,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,0,8,-8,-8,0,0,24,24,0,0,0,0,0,0,0,0,0,0,8,0,
0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,0,-8,-8,8,0,0,24,24,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-4,0,-4,-4,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,0,-8,-8,8,0,0,24,24,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-4,0,12,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,0,-8,-8,8,0,0,24,24,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,-4,12,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,0,-8,-8,8,0,0,24,24,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[32,32,-8,0,0,0,0,8,-32,0,0,-8,8,
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( 3, 8)(11,12)(13,14)(19,20)(45,48)(50,51)(52,53)(57,58)(61,64)(66,67)(68,69)
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ALF("HNN2","HN",[1,3,2,6,2,3,6,3,3,3,2,3,6,6,2,3,7,6,6,7,6,7,8,3,19,18,19,
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31,30,4,15,14,31,15,15,15,14,15,31,31,31,14,15,30,31],[
"fusion map is unique up to table automorphisms"
]);

MOT("[7^6]:(6x6)",
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0,0,0,0,0,0,-6,1,-6,1,1,0,0,-6,1,0,0,0,0,0,-6,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[91,19]],
[TENSOR,[91,2]],
[TENSOR,[91,3]],
[TENSOR,[91,20]],
[TENSOR,[91,21]],[882,-147,0,0,0,0,0,-21,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-18,3,3,3,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[97,19]],[882,-147,0,0,0,0,0,21,-7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-18,3,3,-4,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[99,19]]],
[
( 24, 45)( 25, 46)( 26, 38)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 43)
( 32, 44)( 47, 93)( 48, 99)( 49,100)( 50, 97)( 51, 98)( 52, 96)( 53, 95)
( 54, 94)( 55, 83)( 56, 84)( 57, 92)( 58, 90)( 59, 91)( 60, 88)( 61, 89)
( 62, 86)( 63, 87)( 64, 85)( 70, 81)( 71, 82)( 72, 79)( 73, 80)
]);
ALF("[7^6]:(6x6)","M",[1,20,20,19,19,20,19,19,20,19,20,20,20,19,19,20,19,
19,20,19,19,19,20,15,131,4,71,71,71,70,71,71,3,49,48,49,48,4,71,71,71,70,
71,71,15,131,18,18,130,18,130,18,18,18,6,72,18,6,72,18,130,6,72,18,3,49,
48,48,49,15,131,15,131,3,48,49,49,48,15,131,15,131,6,72,18,6,72,18,130,6,
72,18,18,18,18,18,18,130,18,130],[ 
"fusion determined by factorization through 7^(2+1+2):GL2(7)"
]);
ALN("[7^6]:(6x6)",["MN7"]);

MOT("(3x13:6).2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[468,39,36,36,36,36,36,234,39,39,18,18,18,18,18,12,12,12,12,12,12],
[,[1,2,4,6,1,4,6,8,9,10,12,14,8,12,14,3,5,7,3,5,7],[1,2,5,1,5,1,5,1,2,2,5,1,5,
1,5,17,20,17,20,17,20],,,,,,,,,,[1,1,3,4,5,6,7,8,8,8,11,12,13,14,15,16,17,18,
19,20,21]],
0,
[( 9,10),( 3, 7)( 4, 6)(11,15)(12,14)(16,18)(19,21),(16,19)(17,20)(18,21)],
["ConstructIndexTwoSubdirectProduct","C3","S3","13:6","13:12",[29,31..39],(),
()]);
ALF("(3x13:6).2","S3",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3]);
ALF("(3x13:6).2","13:12",[1,2,4,6,8,10,12,1,2,2,4,6,8,10,12,3,5,7,9,11,13]);
ALF("(3x13:6).2","3.Fi22.2",[1,81,42,13,7,13,42,2,82,83,42,13,8,13,42,145,
117,145,145,117,145],[
"fusion map is unique up to table aut."
]);
ALF("(3x13:6).2","3.Suz.2",[1,58,31,11,5,11,31,2,59,60,31,11,6,11,31,94,
79,94,94,79,94],[
"fusion map is unique up to table aut."
]);
ALF("(3x13:6).2","Th",[1,23,9,5,2,5,9,3,47,48,11,4,10,4,11,22,7,22,22,7,
22],[
"fusion map is unique up to table aut."
]);
ALN("(3x13:6).2",["ThN13"]);

MOT("Fi23N3",
[
"origin: Dixon's Algorithm,\n",
"Sylow 3 normalizer in Fi23 (computed from a representation of this group)\n",
"and in B (see [Wil98])"
],
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,78732,39366,13122,78732,78732,78732,78732,78732,78732,26244,26244,26244,13122
,13122,78732,78732,78732,39366,39366,39366,26244,26244,26244,26244,26244,26244
,13122,13122,13122,13122,13122,13122,13122,6561,26244,26244,26244,4374,1458,
486,26244,13122,4374,1458,1458,1458,1458,486,486,486,8748,4374,1458,486,1458,
729,486,486,486,486,486,243,243,243,26244,26244,26244,26244,26244,26244,8748,
8748,8748,4374,4374,1458,729,486,1458,1458,1458,1458,1458,729,729,486,486,486,
243,162,162,162,162,27,1944,972,972,972,972,324,324,324,324,324,324,324,324,
324,324,162,108,54,54,54,54,1944,1944,972,972,972,972,972,972,972,972,324,324,
324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,162,
162,108,108,54,54,54,54,54,54,54,54,157464,1944,1944,1944,78732,26244,8748,
8748,8748,8748,8748,8748,8748,2916,2916,2916,2916,2916,2916,2916,2916,2916,
2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,1458,1458,1458,
1458,1458,1458,1458,1458,1458,1458,972,972,972,972,972,972,972,972,972,972,972
,972,972,972,972,972,972,972,972,972,972,486,324,324,324,324,324,324,324,324,
324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,
324,324,324,162,162,162,162,108,108,108,54,54,54,162,162,162,162,162,162,54,54
,54,54,54,54,54,54,54,54,54,54],
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29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,
105,1,80,79,81,2,84,83,82,46,48,47,77,78,76,5,86,12,87,94,92,49,1,1,7,4,6,8,3,
11,9,10,12,32,37,27,33,28,36,26,35,34,15,16,17,20,18,19,12,21,22,23,14,13,52,
62,54,64,59,60,61,70,71,72,1,1,1,1,2,3,16,15,17,7,6,8,4,78,77,76,9,11,10,20,19
,18,22,21,23,28,36,33,35,34,26,37,27,32,24,31,43,39,42,40,29,44,30,38,3,18,20,
19,46,48,47,2,46,48,47,82,83,84,80,79,81,4,27,28,26,85,16,17,15,5,23,22,21,10,
9,11,80,79,81,82,84,83,77,76,78,52,6,5,7,8,36,37,32,34,35,33,25,53,89,41,52,62
,62,55,63,65,91,90,50,93,98,97,56,57,58,103,104,102,51,99,101,68,66,69],[1,1,1
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128,128,128,128,128,128,128,128,127,128,127,128,127,128,131,131,131,134,134,
134,169,170,171,172,169,169,169,169,169,169,169,169,169,169,169,169,169,169,
169,169,169,169,169,169,169,169,169,169,169,169,169,169,169,169,169,169,169,
169,169,169,169,169,169,169,170,170,170,170,171,171,171,171,169,169,169,169,
169,169,169,169,169,172,172,172,172,169,170,170,170,170,170,170,170,170,170,
170,171,171,171,171,171,171,171,171,171,171,172,172,172,172,172,172,172,172,
172,172,170,171,169,172,170,171,172,170,171,172,174,174,174,173,173,173,213,
213,213,219,219,219,181,179,180,230,230,230]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
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19,20,27,20,27,21,19,18,23,15,23,18,23,23,18,15,21,27,20,19,23,26,22,21,
22,27,25,28,28,25,19,28,25,21,28,27,26,25,22,19,22,19,22,25,28,26,27,22,
28,21,25,28,28,23,28,22,22,22,28,28,28,67,67,67,67,67,66,68,72,69,69,68,
72,67,67,73,68,72,69],[
"by factorization through Fi23M8"
]);
ALF("Fi23N3","B",[1,7,7,7,6,7,6,7,6,7,7,6,7,7,7,6,6,7,7,6,7,6,7,7,7,7,7,6,
7,6,7,6,6,7,7,6,7,7,7,7,7,7,7,6,7,6,7,7,46,47,47,6,7,7,7,47,46,46,47,46,
46,6,7,7,7,46,46,47,46,46,46,47,47,46,46,6,6,7,6,7,7,7,6,7,7,7,7,7,7,47,
47,46,47,47,47,46,47,47,47,46,47,46,46,47,131,5,28,24,28,29,29,27,28,27,
29,28,24,29,27,27,29,27,29,95,96,96,5,5,24,28,29,28,28,29,24,28,27,27,29,
29,24,27,27,29,28,28,28,27,27,27,29,29,27,28,24,29,29,29,27,27,29,29,95,
96,96,96,96,95,2,5,5,5,23,23,21,23,20,21,23,23,23,23,21,20,21,23,23,21,23,
23,21,23,23,21,21,21,23,23,23,23,23,20,23,23,23,23,23,23,23,21,21,23,29,
28,24,28,24,28,29,28,21,23,23,23,21,23,23,21,23,29,28,24,28,23,24,27,29,
27,28,27,29,29,27,28,29,27,29,29,28,24,27,27,28,27,28,27,27,29,24,28,27,
29,29,27,29,29,23,29,27,27,27,29,29,29,93,93,93,93,93,92,95,96,96,96,95,
96,93,93,93,95,96,96],[
"by factorization through Fi23M8 and Fi23"
]);
ALN("Fi23N3",["BN3"]);

LIBTABLE.LOADSTATUS.ctosylno:="userloaded";

#############################################################################
##
#E