Quelle targetsQuotient.gi Sprache: unbekannt

#############################################################################
##  targetsQuotient.gi
#############################################################################
##
##  This file is part of the LINS package.
##
##  This file's authors include Friedrich Rober.
##
##  Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-2.0-or-later
##
#############################################################################

#############################################################################
##  LINS_TargetsQuotient
#############################################################################
##  Usage:
##
##  The main function `LowIndexNormalSubgroupsSearch` calls the function
##
##                      `LINS_FindTQuotients`
##
##  with the argument `targets` set to this.
#############################################################################
##  Description:
##
##  This is a pregenerated list following the specifications
##  for the argument `targets` in the function `LINS_FindTQuotients`.
##
##  The list was computed by the code in `addGroup.gi`.
##
##  Let $T$ be a non-abelian simple group.
##  Then the pregenerated list `LINS_TargetsQuotient` contains
##  information on any subgroup $Q$ of $Aut(T x T x ... x T)$,
##  such that $(T x T x ... x T)$ is a subgroup of $Q$
##  and $Q$ acts transitively on the set of copies of $T$,
##  with group order $|Q|$ up to the maximum index bound `LINS_MaxIndex`.
##
##  Let $Q$ be such a group of interest,
##  then the information about $Q$ consists of the following:
##
##  - 1 : the group order $|Q|$
##  - 2 : an index of some non-trivial subgroup $S < Q$,
##        that has trivial core in $Q$
##  - 3 : name of the group $T ^ d$
##
##  The list `LINS_TargetsQuotient` is sorted by information $1$.
#############################################################################

BindGlobal("LINS_TargetsQuotient_Index", 10000000);

BindGlobal("LINS_TargetsQuotient",
List(
[ [        60, "[ (1,2,3,4,5), (3,4,5) ]", "A5^1" ],
  [       120, "[ (4,5), (1,2,3,4,5) ]", "A5^1" ],
  [       168, "[ (3,7,5)(4,8,6), (1,2,6)(3,4,8) ]", "PSL(2,7)^1" ],
  [       336, "[ (3,8,7,6,5,4), (1,2,6)(3,4,8) ]", "PSL(2,7)^1" ],
  [       360, "[ (1,2,3,4,5)(8,10,11,9,12), (4,5,6)(7,12,10)(8,11,9) ]", "A6^1" ],
  [       504, "[ (3,8,6,4,9,7,5), (1,2,3)(4,7,5)(6,9,8) ]", "PSL(2,8)^1" ],
  [       660, "[ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]", "PSL(2,11)^1" ],
  [       720, "[ (1,7,2,8,3,9,4,10)(5,11,6,12), (1,2,3,4,5)(8,10,11,9,12) ]", "A6^1" ],
  [       720, "[ (1,9,4,8,3,7,2,10)(5,12,6,11), (1,2,3,4,5)(8,10,11,9,12) ]", "A6^1" ],
  [       720, "[ (5,6)(7,9)(8,10)(11,12), (1,2,3,4,5)(8,10,11,9,12) ]", "A6^1" ],
  [      1092, "[ (3,13,11,9,7,5)(4,14,12,10,8,6), (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]", "PSL(2,13)^1" ],
  [      1320, "[ (3,12,11,10,9,8,7,6,5,4), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ]", "PSL(2,11)^1" ],
  [      1440, "[ (1,7,2,8,3,9,4,10)(5,11,6,12), (5,6)(7,9)(8,10)(11,12), (1,2,3,4,5)(8,10,11,9,12) ]", "A6^1" ],
  [      1512, "[ (4,5,7)(6,9,8), (3,8,6,4,9,7,5), (1,2,3)(4,7,5)(6,9,8) ]", "PSL(2,8)^1" ],
  [      2184, "[ (3,14,13,12,11,10,9,8,7,6,5,4), (1,2,9)(3,8,10)(4,5,12)(6,13,14) ]", "PSL(2,13)^1" ],
  [      2448, "[ (3,17,15,13,11,9,7,5)(4,18,16,14,12,10,8,6), (1,2,11)(3,13,9)(4,15,6)(5,8,12)(7,18,16)(10,14,17) ]", "PSL(2,17)^1" ],
  [      2520, "[ (1,2,3,4,5,6,7), (5,6,7) ]", "A7^1" ],
  [      3420, "[ (3,19,17,15,13,11,9,7,5)(4,20,18,16,14,12,10,8,6), (1,2,12)(3,11,13)(4,17,6)(5,14,8)(7,20,18)(10,19,16) ]", "PSL(2,19)^1" ],
  [      4080, "[ (3,16,14,13,11,4,8,6,17,15,5,12,10,9,7), (1,2,3)(6,14,8)(7,11,10)(9,17,15)(12,16,13) ]", "PSL(2,16)^1" ],
  [      4896, "[ (3,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,11)(3,13,9)(4,15,6)(5,8,12)(7,18,16)(10,14,17) ]", "PSL(2,17)^1" ],
  [      5040, "[ (6,7), (1,2,3,4,5,6,7) ]", "A7^1" ],
  [      5616, "[ (5,8,11)(6,9,12)(7,10,13)(15,24,21)(16,26,22)(17,25,23), (1,2,5)(3,8,7)(4,11,6)(9,10,13)(14,15,18)(16,21,20)(17,24,19)(22,23,26) ]", "PSL(3,3)^1" ],
  [      6048, "[ (3,4,6,10,12,18,19,23)(5,8,13,20,17,11,16,7)(9,14,21,15,22,24,26,28)(25,27), (1,2,3,5,9,15,16,18)(4,7,12,19,24,27,26,23)(6,11,17,13,8,10,14,21)(20,25) ]", "PSU(3,3)^1" ],
  [      6072, "[ (3,23,21,19,17,15,13,11,9,7,5)(4,24,22,20,18,16,14,12,10,8,6), (1,2,14)(3,12,16)(4,18,9)(5,20,6)(7,13,11)(8,23,22)(10,24,19)(15,21,17) ]", "PSL(2,23)^1" ],
  [      6840, "[ (3,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,12)(3,11,13)(4,17,6)(5,14,8)(7,20,18)(10,19,16) ]", "PSL(2,19)^1" ],
  [      7200, "[ (1,6,5,7,4,8,3,9,2,10), (8,9,10) ]", "A5^2" ],
  [      7800, "[ (3,25,23,6,20,18,5,15,13,4,10,8)(7,26,24,22,21,19,17,16,14,12,11,9), (1,2,5)(3,4,6)(7,18,14)(8,22,9)(10,17,12)(11,25,24)(15,26,19)(16,23,21) ]", "PSL(2,25)^1" ],
  [      7920, "[ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ]", "M11^1" ],
  [      8160, "[ (6,9)(7,12)(8,15)(10,13)(11,16)(14,17), (3,16,14,13,11,4,8,6,17,15,5,12,10,9,7), (1,2,3)(6,14,8)(7,11,10)(9,17,15)(12,16,13) ]", "PSL(2,16)^1" ],
  [      9828, "[ (3,27,25,23,21,19,17,16,14,12,10,8,6)(4,15,13,11,9,7,5,28,26,24,22,20,18), (1,2,4)(5,8,24)(6,21,10)(7,16,15)(9,25,28)(11,13,14)(12,27,23)(17,26,18)(19,20,22) ]", "PSL(2,27)^1" ],
  [     11232, "[ (1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26), (5,8,11)(6,9,12)(7,10,13)(15,24,21)(16,26,22)(17,25,23), (1,2,5)(3,8,7)(4,11,6)(9,10,13)(14,15,18)(16,21,20)(17,24,19)(22,23,26) ]", "PSL(3,3)^1" ],
  [     12096, "[ (3,28,12,15)(4,21,18,26)(5,20,17,7)(6,24,19,14)(8,16,11,13)(9,23,22,10), (3,4,6,10,12,18,19,23)(5,8,13,20,17,11,16,7)(9,14,21,15,22,24,26,28)(25,27), (1,2,3,5,9,15,16,18)(4,7,12,19,24,27,26,23)(6,11,17,13,8,10,14,21)(20,25) ]", "PSU(3,3)^1" ],
  [     12144, "[ (3,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,14)(3,12,16)(4,18,9)(5,20,6)(7,13,11)(8,23,22)(10,24,19)(15,21,17) ]", "PSL(2,23)^1" ],
  [     12180, "[ (3,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,17)(3,16,18)(4,12,21)(5,23,9)(6,7,24)(8,15,14)(10,27,28)(11,29,25)(13,22,30)(19,26,20) ]", "PSL(2,29)^1" ],
  [     14400, "[ (1,6,5,7,4,8,3,10)(2,9), (4,5)(9,10), (8,9,10) ]", "A5^2" ],
  [     14400, "[ (1,6,5,7,4,8,3,9,2,10), (4,5)(9,10), (1,5,4,3,2) ]", "A5^2" ],
  [     14880, "[ (3,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,18)(3,24,12)(4,30,5)(6,32,31)(7,10,22)(8,15,16)(9,11,19)(14,26,29)(17,25,27)(20,21,28) ]", "PSL(2,31)^1" ],
  [     15600, "[ (3,26,25,24,23,22,6,21,20,19,18,17,5,16,15,14,13,12,4,11,10,9,8,7), (1,2,5)(3,4,6)(7,18,14)(8,22,9)(10,17,12)(11,25,24)(15,26,19)(16,23,21) ]", "PSL(2,25)^1" ],
  [     15600, "[ (3,26,6,21,5,16,4,11)(7,10,22,25,17,20,12,15)(8,14,23,9,18,24,13,19), (3,25,23,6,20,18,5,15,13,4,10,8)(7,26,24,22,21,19,17,16,14,12,11,9), (1,2,5)(3,4,6)(7,18,14)(8,22,9)(10,17,12)(11,25,24)(15,26,19)(16,23,21) ]", "PSL(2,25)^1" ],
  [     15600, "[ (7,11)(8,15)(9,19)(10,23)(12,16)(13,20)(14,24)(17,21)(18,25)(22,26), (3,25,23,6,20,18,5,15,13,4,10,8)(7,26,24,22,21,19,17,16,14,12,11,9), (1,2,5)(3,4,6)(7,18,14)(8,22,9)(10,17,12)(11,25,24)(15,26,19)(16,23,21) ]", "PSL(2,25)^1" ],
  [     16320, "[ (4,5)(6,7,9,12)(8,10,15,13)(11,17,16,14), (6,9)(7,12)(8,15)(10,13)(11,16)(14,17), (3,16,14,13,11,4,8,6,17,15,5,12,10,9,7), (1,2,3)(6,14,8)(7,11,10)(9,17,15)(12,16,13) ]", "PSL(2,16)^1" ],
  [     19656, "[ (3,28,27,26,25,24,23,22,21,20,19,18,17,4,16,15,14,13,12,11,10,9,8,7,6,5), (1,2,4)(5,8,24)(6,21,10)(7,16,15)(9,25,28)(11,13,14)(12,27,23)(17,26,18)(19,20,22) ]", "PSL(2,27)^1" ],
  [     20160, "[ (1,2,3,4,5,6,7), (6,7,8) ]", "A8^1" ],
  [     20160, "[ (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [     24360, "[ (3,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,17)(3,16,18)(4,12,21)(5,23,9)(6,7,24)(8,15,14)(10,27,28)(11,29,25)(13,22,30)(19,26,20) ]", "PSL(2,29)^1" ],
  [     25308, "[ (3,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,21)(3,20,22)(4,31,10)(5,34,6)(7,14,24)(8,37,36)(9,23,13)(11,38,32)(12,16,17)(18,28,35)(19,33,29)(25,26,30) ]", "PSL(2,37)^1" ],
  [     25920, "[ (3,4)(6,7)(9,10)(12,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)(27,39)(28,40)(29,35)(30,36)(31,37), (1,5,14,17,27,22,19,36,3)(2,6,32)(4,7,23,20,37,13,16,26,40)(8,24,29,30,39,10,33,11,34)(9,15,35)(12,25,38)(21,28,31) ]", "PSp(4,3)^1" ],
  [     28800, "[ (1,6,5,7,4,8,3,9,2,10), (4,5), (9,10), (8,9,10) ]", "A5^2" ],
  [     29120, "[ (1,28,10,44)(3,50,11,42)(4,43,53,64)(5,9,39,52)(6,36,63,13)(7,51,60,57)(8,33,37,16)(12,24,55,29)(14,30,48,47)(15,19,61,54)(17,59,22,62)(18,23,34,31)(20,38,49,25)(21,26,45,58)(27,32,41,65)(35,46,40,56), (1,2)(3,10)(4,42)(5,18)(6,50)(7,26)(8,58)(9,34)(12,28)(13,45)(14,44)(15,23)(16,31)(17,21)(19,39)(20,38)(22,25)(24,61)(27,60)(29,65)(30,55)(32,33)(35,52)(36,49)(37,59)(40,54)(41,62)(43,53)(46,48)(47,56)(51,63)(57,64) ]", "Sz(8)^1" ],
  [     29484, "[ (5,7,13)(6,10,21)(8,16,14)(9,18,22)(11,24,15)(12,27,23)(17,19,25)(20,28,26), (3,27,25,23,21,19,17,16,14,12,10,8,6)(4,15,13,11,9,7,5,28,26,24,22,20,18), (1,2,4)(5,8,24)(6,21,10)(7,16,15)(9,25,28)(11,13,14)(12,27,23)(17,26,18)(19,20,22) ]", "PSL(2,27)^1" ],
  [     29760, "[ (3,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,18)(3,24,12)(4,30,5)(6,32,31)(7,10,22)(8,15,16)(9,11,19)(14,26,29)(17,25,27)(20,21,28) ]", "PSL(2,31)^1" ],
  [     31200, "[ (7,11)(8,15)(9,19)(10,23)(12,16)(13,20)(14,24)(17,21)(18,25)(22,26), (3,26,25,24,23,22,6,21,20,19,18,17,5,16,15,14,13,12,4,11,10,9,8,7), (1,2,5)(3,4,6)(7,18,14)(8,22,9)(10,17,12)(11,25,24)(15,26,19)(16,23,21) ]", "PSL(2,25)^1" ],
  [     32736, "[ (3,32,30,28,26,24,22,20,18,16,14,12,10,8,6,4,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5), (1,2,3)(4,16,20)(5,29,6)(7,24,9)(8,32,31)(10,12,18)(11,14,15)(13,30,28)(17,21,33)(19,25,27)(22,23,26) ]", "PSL(2,32)^1" ],
  [     34440, "[ (3,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,23)(3,37,9)(4,24,21)(5,31,13)(6,36,7)(8,12,29)(10,40,39)(11,20,18)(14,16,19)(15,41,33)(17,34,38)(22,42,25)(26,35,28)(27,30,32) ]", "PSL(2,41)^1" ],
  [     39732, "[ (3,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,24)(3,39,9)(4,12,35)(5,14,32)(6,19,26)(7,33,11)(8,25,18)(10,20,21)(13,36,44)(15,41,37)(16,34,43)(22,29,42)(23,40,30)(27,28,38) ]", "PSL(2,43)^1" ],
  [     40320, "[ (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [     40320, "[ (1,22)(2,23)(3,24)(4,26)(5,25)(6,27)(7,28)(8,30)(9,29)(10,31)(11,32)(12,34)(13,33)(14,39)(15,40)(16,42)(17,41)(18,35)(19,36)(20,38)(21,37), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [     40320, "[ (4,5)(8,9)(12,13)(14,18)(15,19)(16,21)(17,20)(25,26)(29,30)(33,34)(35,39)(36,40)(37,42)(38,41), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [     40320, "[ (7,8), (1,2,3,4,5,6,7) ]", "A8^1" ],
  [     50616, "[ (3,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,21)(3,20,22)(4,31,10)(5,34,6)(7,14,24)(8,37,36)(9,23,13)(11,38,32)(12,16,17)(18,28,35)(19,33,29)(25,26,30) ]", "PSL(2,37)^1" ],
  [     51840, "[ (6,7)(8,11)(9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)(26,29)(27,31)(28,30)(33,34)(35,38)(36,40)(37,39), (3,4)(6,7)(9,10)(12,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)(27,39)(28,40)(29,35)(30,36)(31,37), (1,5,14,17,27,22,19,36,3)(2,6,32)(4,7,23,20,37,13,16,26,40)(8,24,29,30,39,10,33,11,34)(9,15,35)(12,25,38)(21,28,31) ]", "PSp(4,3)^1" ],
  [     51888, "[ (3,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,26)(3,8,44)(4,34,17)(5,43,7)(6,28,21)(9,47,45)(10,16,29)(11,32,12)(13,15,27)(14,22,19)(18,48,35)(20,41,40)(23,36,42)(24,46,31)(25,37,39)(30,38,33) ]", "PSL(2,47)^1" ],
  [     56448, "[ (1,5)(2,8)(3,12)(4,14)(6,16)(7,19)(9,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,33)(20,34)(22,36)(24,37)(26,38)(28,39)(30,40)(32,41)(35,42), (1,20,32)(2,13,24)(3,9,4)(6,11,22)(7,28,35)(10,18,26)(15,17,30), (1,32,15)(2,22,3)(4,35,30)(6,24,7)(9,20,18)(10,17,11)(13,26,28) ]", "PSL(2,7)^2" ],
  [     58800, "[ (3,49,47,45,8,42,40,38,7,35,33,31,6,28,26,24,5,21,19,17,4,14,12,10)(9,50,48,46,44,43,41,39,37,36,34,32,30,29,27,25,23,22,20,18,16,15,13,11), (1,2,6)(3,4,8)(9,25,33)(10,20,37)(11,32,24)(12,15,41)(13,38,16)(14,30,23)(17,31,19)(18,44,47)(21,46,43)(22,39,49)(26,34,50)(27,48,35)(28,42,40)(29,45,36) ]", "PSL(2,49)^1" ],
  [     58968, "[ (5,7,13)(6,10,21)(8,16,14)(9,18,22)(11,24,15)(12,27,23)(17,19,25)(20,28,26), (3,28,27,26,25,24,23,22,21,20,19,18,17,4,16,15,14,13,12,11,10,9,8,7,6,5), (1,2,4)(5,8,24)(6,21,10)(7,16,15)(9,25,28)(11,13,14)(12,27,23)(17,26,18)(19,20,22) ]", "PSL(2,27)^1" ],
  [     60480, "[ (7,9,8)(10,18,14)(11,21,16)(12,19,17)(13,20,15)(28,29,30)(31,35,39)(32,37,42)(33,38,40)(34,36,41), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [     62400, "[ (3,4,6,10,18,31,49,56,63,5,8,14,25,42,58)(7,12,22,38,41,32,50,48,37,55,11,20,34,13,24)(9,16,28,45,61,64,59,17,29,23,40,54,62,65,15)(19,33,51,52,35,53,27,44,60,26,30,47,57,46,39)(21,36,43), (1,2,3,5,9,17,30,48,55,20,35,54,45,58,63)(4,7,13,18,32,38,56,60,61,42,59,62,8,15,27)(6,11,21,37,49,47,50,51,29,46,33,40,57,34,52)(10,19,12,23,22,39,31,28,36,53,25,14,26,43,16)(24,41,44) ]", "PSU(3,4)^1" ],
  [     68880, "[ (3,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,23)(3,37,9)(4,24,21)(5,31,13)(6,36,7)(8,12,29)(10,40,39)(11,20,18)(14,16,19)(15,41,33)(17,34,38)(22,42,25)(26,35,28)(27,30,32) ]", "PSL(2,41)^1" ],
  [     74412, "[ (3,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,29)(3,28,30)(4,12,45)(5,34,22)(6,47,8)(7,19,35)(9,10,42)(11,52,50)(13,46,54)(14,20,27)(15,25,21)(16,48,49)(17,26,18)(23,39,51)(24,53,36)(31,38,44)(32,41,40)(33,43,37) ]", "PSL(2,53)^1" ],
  [     79464, "[ (3,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,24)(3,39,9)(4,12,35)(5,14,32)(6,19,26)(7,33,11)(8,25,18)(10,20,21)(13,36,44)(15,41,37)(16,34,43)(22,29,42)(23,40,30)(27,28,38) ]", "PSL(2,43)^1" ],
  [     80640, "[ (4,5)(8,9)(12,13)(14,18)(15,19)(16,21)(17,20)(25,26)(29,30)(33,34)(35,39)(36,40)(37,42)(38,41), (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [     87360, "[ (4,7,5)(6,8,9)(12,15,13)(14,16,17)(18,42,26)(19,43,27)(20,47,29)(21,44,31)(22,48,33)(23,45,28)(24,49,30)(25,46,32)(34,50,58)(35,51,59)(36,55,61)(37,52,63)(38,56,65)(39,53,60)(40,57,62)(41,54,64), (1,28,10,44)(3,50,11,42)(4,43,53,64)(5,9,39,52)(6,36,63,13)(7,51,60,57)(8,33,37,16)(12,24,55,29)(14,30,48,47)(15,19,61,54)(17,59,22,62)(18,23,34,31)(20,38,49,25)(21,26,45,58)(27,32,41,65)(35,46,40,56), (1,2)(3,10)(4,42)(5,18)(6,50)(7,26)(8,58)(9,34)(12,28)(13,45)(14,44)(15,23)(16,31)(17,21)(19,39)(20,38)(22,25)(24,61)(27,60)(29,65)(30,55)(32,33)(35,52)(36,49)(37,59)(40,54)(41,62)(43,53)(46,48)(47,56)(51,63)(57,64) ]", "Sz(8)^1" ],
  [     95040, "[ (3,7,11,8)(4,10,5,6)(13,19)(14,23)(15,17,20,21)(16,22,24,18), (1,2,3,4,5,6,7,8,9,10,11)(14,18,22,17,24,16,20,23,19,15,21), (1,12)(2,11)(3,6)(4,8)(5,9)(7,10)(13,19)(14,24)(15,23)(16,18)(17,20)(21,22) ]", "M12^1" ],
  [    102660, "[ (3,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,32)(3,31,33)(4,40,23)(5,26,36)(6,48,13)(7,50,10)(8,15,44)(9,39,19)(11,22,34)(12,18,37)(14,57,54)(16,58,51)(17,21,29)(20,49,56)(24,60,41)(25,55,45)(27,46,52)(28,38,59)(30,42,53)(35,43,47) ]", "PSL(2,59)^1" ],
  [    103776, "[ (3,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,26)(3,8,44)(4,34,17)(5,43,7)(6,28,21)(9,47,45)(10,16,29)(11,32,12)(13,15,27)(14,22,19)(18,48,35)(20,41,40)(23,36,42)(24,46,31)(25,37,39)(30,38,33) ]", "PSL(2,47)^1" ],
  [    112896, "[ (1,5)(2,8)(3,12)(4,14)(6,16)(7,19)(9,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,33)(20,34)(22,36)(24,37)(26,38)(28,39)(30,40)(32,41)(35,42), (2,24,6,28)(3,4,30,18,10,11,13,7)(8,37)(9,35,22,26,17,20,32,15)(12,23)(14,33)(16,39)(19,25)(21,38)(29,31)(34,41)(36,42), (1,20,32)(2,13,24)(3,9,4)(6,11,22)(7,28,35)(10,18,26)(15,17,30) ]", "PSL(2,7)^2" ],
  [    112896, "[ (1,5)(2,8,24,37,6,16,28,39)(3,12,4,14,30,40,18,33,10,23,11,25,13,27,7,19)(9,21,35,42,22,36,26,38,17,31,20,34,32,41,15,29), (2,24,6,28)(3,4,30,18,10,11,13,7)(8,37)(9,35,22,26,17,20,32,15)(12,23)(14,33)(16,39)(19,25)(21,38)(29,31)(34,41)(36,42), (5,12,23)(8,19,33)(14,25,37)(16,29,38)(21,31,39)(27,36,42)(34,41,40) ]", "PSL(2,7)^2" ],
  [    113460, "[ (3,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,33)(3,32,34)(4,27,38)(5,11,53)(6,21,42)(7,46,16)(8,12,49)(9,31,29)(10,44,15)(13,55,61)(14,19,36)(17,54,58)(18,25,26)(20,59,50)(22,56,51)(24,45,60)(28,39,62)(30,47,52)(35,57,37)(40,41,48) ]", "PSL(2,61)^1" ],
  [    117600, "[ (3,50,49,48,47,46,45,44,8,43,42,41,40,39,38,37,7,36,35,34,33,32,31,30,6,29,28,27,26,25,24,23,5,22,21,20,19,18,17,16,4,15,14,13,12,11,10,9), (1,2,6)(3,4,8)(9,25,33)(10,20,37)(11,32,24)(12,15,41)(13,38,16)(14,30,23)(17,31,19)(18,44,47)(21,46,43)(22,39,49)(26,34,50)(27,48,35)(28,42,40)(29,45,36) ]", "PSL(2,49)^1" ],
  [    117600, "[ (3,50,8,43,7,36,6,29,5,22,4,15)(9,14,44,49,37,42,30,35,23,28,16,21)(10,20,45,13,38,48,31,41,24,34,17,27)(11,26,46,19,39,12,32,47,25,40,18,33), (3,49,47,45,8,42,40,38,7,35,33,31,6,28,26,24,5,21,19,17,4,14,12,10)(9,50,48,46,44,43,41,39,37,36,34,32,30,29,27,25,23,22,20,18,16,15,13,11), (1,2,6)(3,4,8)(9,25,33)(10,20,37)(11,32,24)(12,15,41)(13,38,16)(14,30,23)(17,31,19)(18,44,47)(21,46,43)(22,39,49)(26,34,50)(27,48,35)(28,42,40)(29,45,36) ]", "PSL(2,49)^1" ],
  [    117600, "[ (9,15)(10,21)(11,27)(12,33)(13,39)(14,45)(16,22)(17,28)(18,34)(19,40)(20,46)(23,29)(24,35)(25,41)(26,47)(30,36)(31,42)(32,48)(37,43)(38,49)(44,50), (3,49,47,45,8,42,40,38,7,35,33,31,6,28,26,24,5,21,19,17,4,14,12,10)(9,50,48,46,44,43,41,39,37,36,34,32,30,29,27,25,23,22,20,18,16,15,13,11), (1,2,6)(3,4,8)(9,25,33)(10,20,37)(11,32,24)(12,15,41)(13,38,16)(14,30,23)(17,31,19)(18,44,47)(21,46,43)(22,39,49)(26,34,50)(27,48,35)(28,42,40)(29,45,36) ]", "PSL(2,49)^1" ],
  [    120960, "[ (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42), (7,8,9)(10,14,18)(11,16,21)(12,17,19)(13,15,20)(28,30,29)(31,39,35)(32,42,37)(33,40,38)(34,41,36), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [    120960, "[ (4,5)(8,9)(12,13)(14,18)(15,19)(16,21)(17,20)(25,26)(29,30)(33,34)(35,39)(36,40)(37,42)(38,41), (7,8,9)(10,14,18)(11,16,21)(12,17,19)(13,15,20)(28,30,29)(31,39,35)(32,42,37)(33,40,38)(34,41,36), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [    120960, "[ (7,9,8)(10,18,14)(11,21,16)(12,19,17)(13,20,15)(28,29,30)(31,35,39)(32,37,42)(33,38,40)(34,36,41), (1,22)(2,23)(3,24)(4,26)(5,25)(6,27)(7,28)(8,30)(9,29)(10,31)(11,32)(12,34)(13,33)(14,39)(15,40)(16,42)(17,41)(18,35)(19,36)(20,38)(21,37), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [    124800, "[ (3,55,31,24,8,41)(4,13,49,38,14,37)(5,7,58,32,18,11)(6,22,56,48,25,34)(9,51,64,44,40,57)(10,50,63,20,42,12)(15,46,61,52,23,60)(16,27,59,47,54,33)(17,19,62,53,28,30)(21,36,43)(26,45,39,29,35,65), (3,4,6,10,18,31,49,56,63,5,8,14,25,42,58)(7,12,22,38,41,32,50,48,37,55,11,20,34,13,24)(9,16,28,45,61,64,59,17,29,23,40,54,62,65,15)(19,33,51,52,35,53,27,44,60,26,30,47,57,46,39)(21,36,43), (1,2,3,5,9,17,30,48,55,20,35,54,45,58,63)(4,7,13,18,32,38,56,60,61,42,59,62,8,15,27)(6,11,21,37,49,47,50,51,29,46,33,40,57,34,52)(10,19,12,23,22,39,31,28,36,53,25,14,26,43,16)(24,41,44) ]", "PSU(3,4)^1" ],
  [    126000, "[ (3,4,6,10,17,31,33,51)(5,8,14,25,45,13,23,42)(7,12,21,38,55,86,77,92)(9,16,29,52,81,83,111,73)(11,19,34,58,88,22,40,67)(15,27,44,71,46,72,70,101)(18,32,35,59,89,100,116,125)(20,36,61,91,114,126,119,105)(24,39,66,98)(26,47,74,103,80,108,122,57)(28,50,48,76,79,30,54,84)(37,63,94,118,68,99,95,115)(41,64,96,75,104,43,69,85)(49,78,106,62,93,117,65,90)(53,82,109,102,121,123,60,56)(87,113,110,124,112,97,120,107), (1,2,3,5,9)(4,7,13,24,44)(6,11,20,37,64)(8,15,28,51,81)(10,18,33,57,87)(12,22,41,68,100)(14,26,48,77,105)(16,30,55,42,17)(19,35,60,58,34)(21,39,25,46,73)(23,43,70,76,93)(27,49,79,107,122)(29,53,83,112,117)(31,56,86,108,123)(32,52,59,90,101)(36,62,94,89,66)(38,65,97,50,80)(45,69,63,95,119)(47,75,98,121,99)(54,85,109,72,96)(61,92,116,126,84)(67,71,102,118,114)(74,103,78,106,120)(82,110,125,113,124)(88,111,91,115,104) ]", "PSU(3,5)^1" ],
  [    148824, "[ (3,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,29)(3,28,30)(4,12,45)(5,34,22)(6,47,8)(7,19,35)(9,10,42)(11,52,50)(13,46,54)(14,20,27)(15,25,21)(16,48,49)(17,26,18)(23,39,51)(24,53,36)(31,38,44)(32,41,40)(33,43,37) ]", "PSL(2,53)^1" ],
  [    150348, "[ (3,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,36)(3,35,37)(4,63,8)(5,21,49)(6,24,45)(7,38,30)(9,68,64)(10,54,11)(12,41,22)(13,19,43)(14,44,17)(15,20,40)(16,26,33)(18,62,61)(23,51,67)(27,48,66)(28,58,55)(29,53,59)(31,60,50)(32,52,57)(34,65,42)(39,46,56) ]", "PSL(2,67)^1" ],
  [    163680, "[ (4,5,7,11,19)(6,9,15,27,20)(8,13,23,12,21)(10,17,31,28,22)(14,25,16,29,24)(18,33,32,30,26), (3,32,30,28,26,24,22,20,18,16,14,12,10,8,6,4,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5), (1,2,3)(4,16,20)(5,29,6)(7,24,9)(8,32,31)(10,12,18)(11,14,15)(13,30,28)(17,21,33)(19,25,27)(22,23,26) ]", "PSL(2,32)^1" ],
  [    175560, "[ (1,17)(2,67)(3,135)(4,83)(5,115)(6,8)(7,210)(9,114)(10,214)(11,149)(12,59)(13,53)(14,119)(15,179)(16,139)(18,169)(19,50)(20,232)(21,109)(22,128)(23,202)(24,82)(25,56)(26,134)(27,196)(28,234)(29,133)(30,102)(31,256)(32,204)(33,123)(34,148)(35,248)(36,164)(37,185)(38,137)(39,177)(40,165)(41,230)(42,113)(44,93)(45,127)(46,198)(47,180)(48,197)(49,239)(51,112)(52,265)(54,88)(55,66)(57,263)(58,62)(60,89)(61,238)(63,258)(64,97)(65,219)(68,186)(69,120)(70,124)(71,242)(72,211)(73,246)(74,175)(75,92)(76,192)(77,153)(78,215)(79,162)(80,183)(81,244)(84,85)(86,132)(87,264)(90,152)(91,103)(94,220)(95,201)(96,108)(98,171)(99,228)(100,178)(101,187)(104,253)(105,141)(106,147)(107,174)(110,247)(111,184)(116,146)(117,154)(118,158)(121,226)(122,157)(125,161)(126,212)(129,155)(130,159)(131,249)(136,235)(138,218)(140,205)(142,176)(143,227)(145,189)(156,181)(160,236)(163,172)(166,217)(167,251)(170,190)(173,237)(182,262)(188,209)(191,243)(193,259)(194,240)(195,224)(199,229)(200,208)(203,255)(213,225)(216,252)(221,257)(223,254)(231,260)(233,245)(250,261), (1,154,190)(2,78,249)(3,139,165)(4,265,119)(5,201,258)(6,187,237)(7,99,124)(8,246,240)(9,96,180)(10,75,36)(11,141,16)(12,174,215)(13,164,58)(14,242,191)(15,140,26)(17,37,118)(18,59,170)(19,65,189)(20,162,172)(22,223,104)(23,117,45)(24,62,256)(25,152,232)(27,72,128)(28,54,196)(29,40,126)(30,238,255)(31,87,251)(32,142,106)(33,202,261)(34,193,205)(35,171,183)(38,57,254)(39,70,143)(41,123,55)(42,145,110)(43,64,134)(44,195,231)(46,56,248)(47,51,184)(48,66,79)(49,50,207)(52,100,83)(53,158,121)(60,211,88)(61,113,132)(63,98,218)(67,136,81)(68,227,213)(69,192,138)(71,175,93)(73,122,160)(74,137,148)(76,263,125)(77,108,101)(80,264,97)(82,178,163)(84,103,167)(85,262,252)(86,216,166)(89,243,244)(91,241,120)(92,235,214)(94,206,102)(95,144,173)(105,159,157)(107,188,197)(109,156,199)(111,135,253)(112,245,150)(114,247,220)(115,198,194)(116,239,177)(130,230,260)(131,161,200)(133,146,176)(147,204,168)(149,222,181)(151,236,212)(153,225,233)(155,217,226)(169,210,219)(179,182,203)(185,209,224)(186,257,234)(208,221,259)(228,229,266) ]", "J_1^1" ],
  [    178920, "[ (3,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,38)(3,32,44)(4,20,55)(5,46,28)(6,42,31)(7,35,37)(8,57,14)(9,12,58)(10,54,15)(11,25,43)(13,17,49)(16,40,23)(18,64,67)(19,68,62)(21,56,72)(22,66,61)(24,29,26)(27,59,63)(30,71,48)(33,51,65)(34,70,45)(36,60,53)(39,41,69)(47,52,50) ]", "PSL(2,71)^1" ],
  [    181440, "[ (1,2,3,4,5,6,7,8,9), (7,8,9) ]", "A9^1" ],
  [    190080, "[ (1,13,5,17)(2,14,3,15,12,24,9,21,6,18,4,16)(7,19,8,20,10,22)(11,23), (3,7,11,8)(4,10,5,6)(13,19)(14,23)(15,17,20,21)(16,22,24,18) ]", "M12^1" ],
  [    194472, "[ (3,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,39)(3,31,47)(4,25,52)(5,44,32)(6,58,17)(7,64,10)(8,16,57)(9,23,49)(11,33,37)(12,56,13)(14,71,68)(15,30,36)(18,28,35)(19,38,24)(20,72,61)(21,62,70)(22,66,65)(26,53,74)(29,55,69)(34,73,46)(40,59,54)(41,45,67)(42,48,63)(43,50,60) ]", "PSL(2,73)^1" ],
  [    205320, "[ (3,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,32)(3,31,33)(4,40,23)(5,26,36)(6,48,13)(7,50,10)(8,15,44)(9,39,19)(11,22,34)(12,18,37)(14,57,54)(16,58,51)(17,21,29)(20,49,56)(24,60,41)(25,55,45)(27,46,52)(28,38,59)(30,42,53)(35,43,47) ]", "PSL(2,59)^1" ],
  [    225792, "[ (1,5)(2,8)(3,12)(4,14)(6,16)(7,19)(9,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,33)(20,34)(22,36)(24,37)(26,38)(28,39)(30,40)(32,41)(35,42), (8,37)(12,23)(14,33)(16,39)(19,25)(21,38)(29,31)(34,41)(36,42), (2,24,6,28)(3,4,30,18,10,11,13,7)(9,35,22,26,17,20,32,15), (5,41,34)(8,37,27)(12,14,21)(16,36,25)(19,42,39)(23,38,33)(29,40,31) ]", "PSL(2,7)^2" ],
  [    226920, "[ (3,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,33)(3,32,34)(4,27,38)(5,11,53)(6,21,42)(7,46,16)(8,12,49)(9,31,29)(10,44,15)(13,55,61)(14,19,36)(17,54,58)(18,25,26)(20,59,50)(22,56,51)(24,45,60)(28,39,62)(30,47,52)(35,57,37)(40,41,48) ]", "PSL(2,61)^1" ],
  [    235200, "[ (9,15)(10,21)(11,27)(12,33)(13,39)(14,45)(16,22)(17,28)(18,34)(19,40)(20,46)(23,29)(24,35)(25,41)(26,47)(30,36)(31,42)(32,48)(37,43)(38,49)(44,50), (3,50,49,48,47,46,45,44,8,43,42,41,40,39,38,37,7,36,35,34,33,32,31,30,6,29,28,27,26,25,24,23,5,22,21,20,19,18,17,16,4,15,14,13,12,11,10,9), (1,2,6)(3,4,8)(9,25,33)(10,20,37)(11,32,24)(12,15,41)(13,38,16)(14,30,23)(17,31,19)(18,44,47)(21,46,43)(22,39,49)(26,34,50)(27,48,35)(28,42,40)(29,45,36) ]", "PSL(2,49)^1" ],
  [    241920, "[ (4,5)(8,9)(12,13)(14,18)(15,19)(16,21)(17,20)(25,26)(29,30)(33,34)(35,39)(36,40)(37,42)(38,41), (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42), (7,8,9)(10,14,18)(11,16,21)(12,17,19)(13,15,20)(28,30,29)(31,39,35)(32,42,37)(33,40,38)(34,41,36), (3,4,5)(7,9,8)(10,14,18)(11,17,20)(12,15,21)(13,16,19)(24,26,25)(28,29,30)(31,39,35)(32,41,38)(33,42,36)(34,40,37), (1,2,6,7,11,3,10)(4,14,8,15,16,20,13)(5,18,9,19,21,17,12)(22,23,28,24,32,31,27)(25,36,41,42,34,39,30)(26,40,38,37,33,35,29) ]", "PSL(3,4)^1" ],
  [    246480, "[ (3,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,42)(3,38,46)(4,34,49)(5,54,28)(6,59,22)(7,41,39)(8,67,12)(9,10,68)(11,58,18)(13,23,51)(14,53,20)(15,40,32)(16,74,75)(17,76,72)(19,21,47)(24,36,27)(25,78,62)(26,73,66)(30,79,56)(31,70,64)(33,61,71)(35,50,80)(37,63,65)(43,77,45)(44,69,52)(48,60,57) ]", "PSL(2,79)^1" ],
  [    249600, "[ (3,29,24,26)(4,40,38,51)(5,54,32,27)(6,62,48,30)(7,47,18,16)(8,65,55,39)(9,13,44,14)(10,15,20,52)(11,33,58,59)(12,46,63,23)(17,34,53,56)(19,25,28,22)(21,36)(31,45,41,35)(37,57,49,64)(42,61,50,60), (3,55,31,24,8,41)(4,13,49,38,14,37)(5,7,58,32,18,11)(6,22,56,48,25,34)(9,51,64,44,40,57)(10,50,63,20,42,12)(15,46,61,52,23,60)(16,27,59,47,54,33)(17,19,62,53,28,30)(21,36,43)(26,45,39,29,35,65), (3,4,6,10,18,31,49,56,63,5,8,14,25,42,58)(7,12,22,38,41,32,50,48,37,55,11,20,34,13,24)(9,16,28,45,61,64,59,17,29,23,40,54,62,65,15)(19,33,51,52,35,53,27,44,60,26,30,47,57,46,39)(21,36,43), (1,2,3,5,9,17,30,48,55,20,35,54,45,58,63)(4,7,13,18,32,38,56,60,61,42,59,62,8,15,27)(6,11,21,37,49,47,50,51,29,46,33,40,57,34,52)(10,19,12,23,22,39,31,28,36,53,25,14,26,43,16)(24,41,44) ]", "PSU(3,4)^1" ],
  [    252000, "[ (3,95)(4,118)(5,103)(6,37)(7,79)(8,26)(9,27)(10,99)(11,43)(12,50)(13,80)(14,108)(15,52)(16,70)(17,94)(18,36)(19,96)(20,59)(21,54)(22,69)(23,47)(24,66)(25,74)(28,55)(29,71)(30,86)(31,115)(32,119)(33,68)(34,85)(35,91)(38,76)(39,98)(40,75)(41,67)(42,122)(44,83)(45,57)(46,73)(48,77)(49,93)(51,63)(53,110)(56,97)(58,104)(60,87)(61,100)(64,88)(65,106)(72,81)(82,107)(84,92)(89,126)(101,111)(102,113)(105,116)(109,112)(114,125)(120,121)(123,124), (3,4,6,10,17,31,33,51)(5,8,14,25,45,13,23,42)(7,12,21,38,55,86,77,92)(9,16,29,52,81,83,111,73)(11,19,34,58,88,22,40,67)(15,27,44,71,46,72,70,101)(18,32,35,59,89,100,116,125)(20,36,61,91,114,126,119,105)(24,39,66,98)(26,47,74,103,80,108,122,57)(28,50,48,76,79,30,54,84)(37,63,94,118,68,99,95,115)(41,64,96,75,104,43,69,85)(49,78,106,62,93,117,65,90)(53,82,109,102,121,123,60,56)(87,113,110,124,112,97,120,107), (1,2,3,5,9)(4,7,13,24,44)(6,11,20,37,64)(8,15,28,51,81)(10,18,33,57,87)(12,22,41,68,100)(14,26,48,77,105)(16,30,55,42,17)(19,35,60,58,34)(21,39,25,46,73)(23,43,70,76,93)(27,49,79,107,122)(29,53,83,112,117)(31,56,86,108,123)(32,52,59,90,101)(36,62,94,89,66)(38,65,97,50,80)(45,69,63,95,119)(47,75,98,121,99)(54,85,109,72,96)(61,92,116,126,84)(67,71,102,118,114)(74,103,78,106,120)(82,110,125,113,124)(88,111,91,115,104) ]", "PSU(3,5)^1" ],
  [    259200, "[ (1,19,3,20,5,24,4,22,6,21)(2,23)(7,18,11,16,10,13,9,15,8,14)(12,17), (16,17,18)(19,24,22)(20,23,21) ]", "A6^2" ],
  [    262080, "[ (3,64,62,60,58,57,55,53,51,10,48,47,45,43,42,40,38,36,8,33,31,4,28,27,25,23,21,6,18,16,14,12,65,63,61,59,11,56,54,52,50,49,5,46,44,9,41,39,37,35,34,32,30,29,7,26,24,22,20,19,17,15,13), (1,2,3)(6,9,7)(8,11,10)(12,18,58)(13,24,51)(14,54,20)(15,35,38)(16,40,33)(17,43,29)(19,59,65)(21,46,22)(23,63,57)(25,36,28)(26,53,64)(27,32,30)(31,56,55)(34,60,48)(37,61,44)(39,42,62)(41,52,49)(45,50,47) ]", "PSL(2,64)^1" ],
  [    265680, "[ (3,81,79,77,75,10,72,70,68,66,9,63,61,59,57,8,54,52,50,48,4,45,43,41,39,7,36,34,32,30,6,27,25,23,21,5,18,16,14,12)(11,82,80,78,76,74,73,71,69,67,65,64,62,60,58,56,55,53,51,49,47,46,44,42,40,38,37,35,33,31,29,28,26,24,22,20,19,17,15,13), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [    285852, "[ (3,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,44)(3,43,45)(4,54,33)(5,17,69)(6,64,21)(7,70,14)(8,30,53)(9,22,60)(10,65,16)(11,41,39)(12,27,52)(13,32,46)(15,26,50)(18,81,74)(19,71,83)(20,40,31)(23,78,72)(24,82,67)(25,29,37)(28,66,79)(34,84,55)(35,58,80)(36,61,76)(38,62,73)(42,56,75)(47,77,49)(48,68,57)(51,59,63) ]", "PSL(2,83)^1" ],
  [    300696, "[ (3,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,36)(3,35,37)(4,63,8)(5,21,49)(6,24,45)(7,38,30)(9,68,64)(10,54,11)(12,41,22)(13,19,43)(14,44,17)(15,20,40)(16,26,33)(18,62,61)(23,51,67)(27,48,66)(28,58,55)(29,53,59)(31,60,50)(32,52,57)(34,65,42)(39,46,56) ]", "PSL(2,67)^1" ],
  [    352440, "[ (3,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,47)(3,31,63)(4,15,78)(5,49,43)(6,22,69)(7,10,80)(8,34,55)(9,29,59)(11,42,44)(12,64,21)(13,18,66)(14,84,87)(16,79,90)(17,53,27)(19,46,32)(20,54,23)(24,37,36)(25,72,88)(26,38,33)(28,76,81)(30,82,73)(35,65,85)(39,60,86)(40,74,71)(41,77,67)(45,89,51)(48,75,62)(50,52,83)(56,68,61)(57,70,58) ]", "PSL(2,89)^1" ],
  [    357840, "[ (3,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,38)(3,32,44)(4,20,55)(5,46,28)(6,42,31)(7,35,37)(8,57,14)(9,12,58)(10,54,15)(11,25,43)(13,17,49)(16,40,23)(18,64,67)(19,68,62)(21,56,72)(22,66,61)(24,29,26)(27,59,63)(30,71,48)(33,51,65)(34,70,45)(36,60,53)(39,41,69)(47,52,50) ]", "PSL(2,71)^1" ],
  [    362880, "[ (8,9), (1,2,3,4,5,6,7,8,9) ]", "A9^1" ],
  [    372000, "[ (3,4,5,6)(8,11,10,9)(12,22)(13,26,15,24)(14,23,16,25)(17,27)(18,31,20,29)(19,28,21,30)(34,37,36,35)(39,40,41,42)(43,53)(44,55,46,57)(45,56,47,54)(48,58)(49,60,51,62)(50,61,52,59), (1,2,7,10,25,3,12,9,20,31,18,21,16,24,4,17,11,30,13,29,28,23,5,22)(6,27,8,15,19,26)(32,33,39,36,54,55,60,56,45,48,42,37,59,51,52,57,50,47,58,41,34,44,43,38)(35,49,62,46,53,40) ]", "PSL(3,5)^1" ],
  [    378000, "[ (3,9,50,31,83,54,6,29,76,51,73,28,17,81,30,4,16,48,33,111,84,10,52,79)(5,74,90,13,57,93,14,80,78,42,47,65,45,122,62,8,103,49,23,26,117,25,108,106)(7,44,63,86,101,95,21,46,118,92,27,37,55,70,99,12,71,94,77,15,115,38,72,68)(11,82,18,22,60,100,34,102,35,67,53,125,88,123,89,19,109,32,40,56,116,58,121,59)(20,87,41,126,97,43,61,110,96,105,107,85,114,112,104,36,113,64,119,120,69,91,124,75)(24,98,66,39), (1,2,3,5,9)(4,7,13,24,44)(6,11,20,37,64)(8,15,28,51,81)(10,18,33,57,87)(12,22,41,68,100)(14,26,48,77,105)(16,30,55,42,17)(19,35,60,58,34)(21,39,25,46,73)(23,43,70,76,93)(27,49,79,107,122)(29,53,83,112,117)(31,56,86,108,123)(32,52,59,90,101)(36,62,94,89,66)(38,65,97,50,80)(45,69,63,95,119)(47,75,98,121,99)(54,85,109,72,96)(61,92,116,126,84)(67,71,102,118,114)(74,103,78,106,120)(82,110,125,113,124)(88,111,91,115,104) ]", "PSU(3,5)^1" ],
  [    388944, "[ (3,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,39)(3,31,47)(4,25,52)(5,44,32)(6,58,17)(7,64,10)(8,16,57)(9,23,49)(11,33,37)(12,56,13)(14,71,68)(15,30,36)(18,28,35)(19,38,24)(20,72,61)(21,62,70)(22,66,65)(26,53,74)(29,55,69)(34,73,46)(40,59,54)(41,45,67)(42,48,63)(43,50,60) ]", "PSL(2,73)^1" ],
  [    443520, "[ (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22), (1,4,5,9,3)(2,8,10,7,6)(12,15,16,20,14)(13,19,21,18,17), (1,21)(2,10,8,6)(3,13,4,17)(5,19,9,18)(11,22)(12,14,16,20) ]", "M22^1" ],
  [    456288, "[ (3,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,51)(3,17,85)(4,43,58)(5,88,12)(6,38,61)(7,89,9)(8,27,70)(10,62,33)(11,20,74)(13,95,93)(14,97,90)(15,25,65)(16,42,47)(18,63,24)(19,56,30)(21,48,36)(22,52,31)(23,29,53)(26,34,45)(28,82,91)(32,75,94)(37,77,87)(39,84,78)(40,92,69)(41,64,96)(44,59,98)(46,83,72)(49,73,79)(50,80,71)(54,81,66)(55,60,86)(57,68,76) ]", "PSL(2,97)^1" ],
  [    492960, "[ (3,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,42)(3,38,46)(4,34,49)(5,54,28)(6,59,22)(7,41,39)(8,67,12)(9,10,68)(11,58,18)(13,23,51)(14,53,20)(15,40,32)(16,74,75)(17,76,72)(19,21,47)(24,36,27)(25,78,62)(26,73,66)(30,79,56)(31,70,64)(33,61,71)(35,50,80)(37,63,65)(43,77,45)(44,69,52)(48,60,57) ]", "PSL(2,79)^1" ],
  [    508032, "[ (1,29)(2,42,20,41)(3,55)(4,48,9,49)(5,31,17,30)(6,37,27,44)(7,45,14,53)(8,35,18,34)(10,40,25,56)(11,43)(12,50,19,54)(13,52,26,38)(15,36,16,47)(21,51,28,39)(22,33,23,32)(24,46), (29,50,45,36,46,33,51)(30,53,37,32,38,48,39)(31,55,42,43,44,35,34)(40,41,56,49,54,47,52) ]", "PSL(2,8)^2" ],
  [    515100, "[ (3,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,53)(3,52,54)(4,84,21)(5,29,75)(6,15,88)(7,23,79)(8,71,30)(9,63,37)(10,42,57)(11,16,82)(12,50,47)(13,60,36)(14,62,33)(17,67,25)(18,91,100)(19,32,58)(20,55,34)(22,102,85)(24,90,95)(26,45,38)(27,83,99)(28,40,41)(31,77,101)(35,98,76)(39,89,81)(43,97,69)(44,92,73)(46,93,70)(48,74,87)(49,64,96)(51,86,72)(56,94,59)(61,80,68)(65,66,78) ]", "PSL(2,101)^1" ],
  [    518400, "[ (1,13,9,19,3,16,10,21)(2,17,12,22,6,14,7,20,5,18,11,24,4,15,8,23), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (1,6,4,3,2)(7,12,8,10,11) ]", "A6^2" ],
  [    518400, "[ (1,13,9,21)(2,18,11,23)(3,16,10,19)(4,15,8,24)(5,17,12,20)(6,14,7,22), (1,9)(2,7,3,8,5,12,4,10,6,11)(13,21)(14,19,15,20,17,24,16,22,18,23), (13,14,15,16,17)(20,22,23,21,24) ]", "A6^2" ],
  [    518400, "[ (1,19,3,20,5,24,4,22,6,21)(2,23)(7,18,11,16,10,13,9,15,8,14)(12,17), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (2,5,3)(7,8,10)(9,11,12) ]", "A6^2" ],
  [    518400, "[ (1,19,3,20,5,24,4,22,6,21)(2,23)(7,18,11,16,10,13,9,15,8,14)(12,17), (1,9)(2,7,3,8,5,12,4,10,6,11)(13,21)(14,19,15,20,17,24,16,22,18,23), (13,14,15,16,17)(20,22,23,21,24) ]", "A6^2" ],
  [    518400, "[ (1,19,3,20,5,24,4,22,6,21)(2,23)(7,18,11,16,10,13,9,15,8,14)(12,17), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (2,5,3)(7,8,10)(9,11,12) ]", "A6^2" ],
  [    518400, "[ (1,21)(2,24,4,20,5,23)(3,22,6,19)(7,17,12,18,11,16,10,13,9,15,8,14), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (16,17,18)(19,24,22)(20,23,21) ]", "A6^2" ],
  [    524160, "[ (4,5)(12,19)(13,26)(14,32)(15,39)(16,46)(17,52)(18,59)(20,27)(21,33)(22,40)(23,47)(24,53)(25,60)(28,34)(29,41)(30,54)(31,61)(35,42)(36,48)(37,55)(38,62)(43,49)(44,56)(45,63)(50,57)(51,64)(58,65), (3,64,62,60,58,57,55,53,51,10,48,47,45,43,42,40,38,36,8,33,31,4,28,27,25,23,21,6,18,16,14,12,65,63,61,59,11,56,54,52,50,49,5,46,44,9,41,39,37,35,34,32,30,29,7,26,24,22,20,19,17,15,13), (1,2,3)(6,9,7)(8,11,10)(12,18,58)(13,24,51)(14,54,20)(15,35,38)(16,40,33)(17,43,29)(19,59,65)(21,46,22)(23,63,57)(25,36,28)(26,53,64)(27,32,30)(31,56,55)(34,60,48)(37,61,44)(39,42,62)(41,52,49)(45,50,47) ]", "PSL(2,64)^1" ],
  [    531360, "[ (11,19)(12,27)(13,35)(14,43)(15,51)(16,59)(17,67)(18,75)(20,28)(21,36)(22,44)(23,52)(24,60)(25,68)(26,76)(29,37)(30,45)(31,53)(32,61)(33,69)(34,77)(38,46)(39,54)(40,62)(41,70)(42,78)(47,55)(48,63)(49,71)(50,79)(56,64)(57,72)(58,80)(65,73)(66,81)(74,82), (3,81,79,77,75,10,72,70,68,66,9,63,61,59,57,8,54,52,50,48,4,45,43,41,39,7,36,34,32,30,6,27,25,23,21,5,18,16,14,12)(11,82,80,78,76,74,73,71,69,67,65,64,62,60,58,56,55,53,51,49,47,46,44,42,40,38,37,35,33,31,29,28,26,24,22,20,19,17,15,13), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [    531360, "[ (3,82,10,73,9,64,8,55,4,46,7,37,6,28,5,19)(11,18,74,81,65,72,56,63,47,54,38,45,29,36,20,27)(12,26,75,17,66,80,57,71,48,62,39,53,30,44,21,35)(13,34,76,25,67,16,58,79,49,70,40,61,31,52,22,43)(14,42,77,33,68,24,59,15,50,78,41,69,32,60,23,51), (3,81,79,77,75,10,72,70,68,66,9,63,61,59,57,8,54,52,50,48,4,45,43,41,39,7,36,34,32,30,6,27,25,23,21,5,18,16,14,12)(11,82,80,78,76,74,73,71,69,67,65,64,62,60,58,56,55,53,51,49,47,46,44,42,40,38,37,35,33,31,29,28,26,24,22,20,19,17,15,13), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [    531360, "[ (3,82,81,80,79,78,77,76,75,74,10,73,72,71,70,69,68,67,66,65,9,64,63,62,61,60,59,58,57,56,8,55,54,53,52,51,50,49,48,47,4,46,45,44,43,42,41,40,39,38,7,37,36,35,34,33,32,31,30,29,6,28,27,26,25,24,23,22,21,20,5,19,18,17,16,15,14,13,12,11), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [    546312, "[ (3,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,54)(3,10,98)(4,73,34)(5,40,66)(6,30,75)(7,24,80)(8,92,11)(9,21,81)(12,23,76)(13,60,38)(14,46,51)(15,49,47)(16,100,97)(17,39,55)(18,64,29)(19,56,36)(20,26,65)(22,31,58)(25,45,41)(27,87,99)(28,84,101)(32,85,96)(33,78,102)(35,104,74)(42,68,103)(43,82,88)(44,90,79)(48,95,70)(50,77,86)(52,89,72)(53,69,91)(57,62,94)(59,93,61)(63,83,67) ]", "PSL(2,103)^1" ],
  [    571704, "[ (3,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,44)(3,43,45)(4,54,33)(5,17,69)(6,64,21)(7,70,14)(8,30,53)(9,22,60)(10,65,16)(11,41,39)(12,27,52)(13,32,46)(15,26,50)(18,81,74)(19,71,83)(20,40,31)(23,78,72)(24,82,67)(25,29,37)(28,66,79)(34,84,55)(35,58,80)(36,61,76)(38,62,73)(42,56,75)(47,77,49)(48,68,57)(51,59,63) ]", "PSL(2,83)^1" ],
  [    604800, "[ (1,58,96,14,36,4,25,71)(2,20,85,42,50,92,64,31)(3,51,5,17,89,34,99,11)(6,70)(7,90,12,19,82,86,54,23)(8,43,37,57,77,75,30,73)(9,52,53,95)(10,59,91,28,97,32,68,40)(13,56,74,78,80,46,38,21)(15,100,63,41,27,67,22,35)(16,69,83,24)(18,33,45,81,55,29,98,60)(26,72,47,62)(39,76)(44,79,94,65,88,61,66,49)(48,84), (1,91,65,44,12,82,54,92,70,63)(2,78,80,85,81,5,73,35,17,24)(3,86,22,40,94,99,8,66,41,20)(4,62,74,57,27,58,97,34,50,55)(6,56,38,19,29,7,59,28,96,95)(9,13,47,10,32,33,11,37,98,67)(14,77,71,23,36,84,49,93,76,79)(15,31,18,45,16,26,72,30,42,60)(21,52,90,53,43,46,69,68,83,64)(25,75,87,89,39,88,51,48,100,61) ]", "J_2^1" ],
  [    612468, "[ (3,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,56)(3,55,57)(4,92,19)(5,9,101)(6,22,87)(7,27,81)(8,70,37)(10,33,72)(11,103,107)(12,86,17)(13,28,74)(14,52,49)(15,29,71)(16,46,53)(18,58,39)(20,108,93)(21,62,32)(23,47,45)(24,43,48)(25,90,106)(26,100,95)(30,51,34)(31,85,105)(35,44,36)(38,84,99)(40,79,102)(41,83,97)(42,104,75)(50,91,80)(54,94,73)(59,66,96)(60,98,63)(61,82,78)(64,69,88)(65,89,67)(68,77,76) ]", "PSL(2,107)^1" ],
  [    647460, "[ (3,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,57)(3,108,6)(4,17,96)(5,52,60)(7,28,82)(8,33,76)(9,89,19)(10,13,94)(11,55,51)(12,71,34)(14,26,77)(15,72,30)(16,53,48)(18,97,110)(20,101,104)(21,22,74)(23,45,49)(24,58,35)(25,105,95)(27,46,44)(29,47,41)(31,36,50)(32,86,107)(37,88,100)(38,81,106)(40,92,93)(42,99,84)(43,102,80)(54,62,109)(56,90,79)(59,103,63)(61,98,66)(64,78,83)(65,69,91)(67,85,73)(68,87,70) ]", "PSL(2,109)^1" ],
  [    648000, "[ (1,15,6)(2,14,7)(3,11,8)(4,12,9)(5,13,10), (11,12,13,14,15), (1,5,4,3,2) ]", "A5^3" ],
  [    704880, "[ (3,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,47)(3,31,63)(4,15,78)(5,49,43)(6,22,69)(7,10,80)(8,34,55)(9,29,59)(11,42,44)(12,64,21)(13,18,66)(14,84,87)(16,79,90)(17,53,27)(19,46,32)(20,54,23)(24,37,36)(25,72,88)(26,38,33)(28,76,81)(30,82,73)(35,65,85)(39,60,86)(40,74,71)(41,77,67)(45,89,51)(48,75,62)(50,52,83)(56,68,61)(57,70,58) ]", "PSL(2,89)^1" ],
  [    721392, "[ (3,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,114,112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,59)(3,47,71)(4,35,82)(5,76,40)(6,27,88)(7,65,49)(8,45,68)(9,13,99)(10,77,34)(11,23,87)(12,85,24)(14,89,18)(15,58,48)(16,51,54)(17,72,32)(19,105,109)(20,80,21)(22,55,44)(25,39,57)(26,52,43)(28,37,56)(29,104,100)(30,91,112)(31,95,107)(33,106,94)(36,83,114)(38,98,97)(41,108,84)(42,113,78)(46,101,86)(50,73,110)(53,111,69)(60,103,70)(61,79,93)(62,81,90)(63,96,74)(64,67,102)(66,92,75) ]", "PSL(2,113)^1" ],
  [    744000, "[ (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62), (3,4,5,6)(8,11,10,9)(12,22)(13,26,15,24)(14,23,16,25)(17,27)(18,31,20,29)(19,28,21,30)(34,37,36,35)(39,40,41,42)(43,53)(44,55,46,57)(45,56,47,54)(48,58)(49,60,51,62)(50,61,52,59), (1,2,7,10,25,3,12,9,20,31,18,21,16,24,4,17,11,30,13,29,28,23,5,22)(6,27,8,15,19,26)(32,33,39,36,54,55,60,56,45,48,42,37,59,51,52,57,50,47,58,41,34,44,43,38)(35,49,62,46,53,40) ]", "PSL(3,5)^1" ],
  [    756000, "[ (3,95)(4,118)(5,103)(6,37)(7,79)(8,26)(9,27)(10,99)(11,43)(12,50)(13,80)(14,108)(15,52)(16,70)(17,94)(18,36)(19,96)(20,59)(21,54)(22,69)(23,47)(24,66)(25,74)(28,55)(29,71)(30,86)(31,115)(32,119)(33,68)(34,85)(35,91)(38,76)(39,98)(40,75)(41,67)(42,122)(44,83)(45,57)(46,73)(48,77)(49,93)(51,63)(53,110)(56,97)(58,104)(60,87)(61,100)(64,88)(65,106)(72,81)(82,107)(84,92)(89,126)(101,111)(102,113)(105,116)(109,112)(114,125)(120,121)(123,124), (3,9,50,31,83,54,6,29,76,51,73,28,17,81,30,4,16,48,33,111,84,10,52,79)(5,74,90,13,57,93,14,80,78,42,47,65,45,122,62,8,103,49,23,26,117,25,108,106)(7,44,63,86,101,95,21,46,118,92,27,37,55,70,99,12,71,94,77,15,115,38,72,68)(11,82,18,22,60,100,34,102,35,67,53,125,88,123,89,19,109,32,40,56,116,58,121,59)(20,87,41,126,97,43,61,110,96,105,107,85,114,112,104,36,113,64,119,120,69,91,124,75)(24,98,66,39), (1,2,3,5,9)(4,7,13,24,44)(6,11,20,37,64)(8,15,28,51,81)(10,18,33,57,87)(12,22,41,68,100)(14,26,48,77,105)(16,30,55,42,17)(19,35,60,58,34)(21,39,25,46,73)(23,43,70,76,93)(27,49,79,107,122)(29,53,83,112,117)(31,56,86,108,123)(32,52,59,90,101)(36,62,94,89,66)(38,65,97,50,80)(45,69,63,95,119)(47,75,98,121,99)(54,85,109,72,96)(61,92,116,126,84)(67,71,102,118,114)(74,103,78,106,120)(82,110,125,113,124)(88,111,91,115,104) ]", "PSU(3,5)^1" ],
  [    786240, "[ (6,7,9)(8,11,10)(12,26,15)(13,39,19)(14,52,22)(16,27,29)(17,40,32)(18,53,35)(20,41,46)(21,54,49)(23,28,56)(24,42,59)(25,55,63)(30,43,33)(31,57,36)(34,44,47)(37,45,60)(38,58,64)(48,61,50)(51,62,65), (3,64,62,60,58,57,55,53,51,10,48,47,45,43,42,40,38,36,8,33,31,4,28,27,25,23,21,6,18,16,14,12,65,63,61,59,11,56,54,52,50,49,5,46,44,9,41,39,37,35,34,32,30,29,7,26,24,22,20,19,17,15,13), (1,2,3)(6,9,7)(8,11,10)(12,18,58)(13,24,51)(14,54,20)(15,35,38)(16,40,33)(17,43,29)(19,59,65)(21,46,22)(23,63,57)(25,36,28)(26,53,64)(27,32,30)(31,56,55)(34,60,48)(37,61,44)(39,42,62)(41,52,49)(45,50,47) ]", "PSL(2,64)^1" ],
  [    871200, "[ (1,13,6,22,7,23,4,14,9,19,12,20)(2,15,8,16,5,17,10,21,3,24,11,18), (2,7,6,5,3)(8,11,9,12,10) ]", "PSL(2,11)^2" ],
  [    885720, "[ (3,121,119,117,115,113,12,110,108,106,104,102,11,99,97,95,93,91,10,88,86,84,82,80,9,77,75,73,71,69,8,66,64,62,60,58,7,55,53,51,49,47,6,44,42,40,38,36,5,33,31,29,27,25,4,22,20,18,16,14)(13,122,120,118,116,114,112,111,109,107,105,103,101,100,98,96,94,92,90,89,87,85,83,81,79,78,76,74,72,70,68,67,65,63,61,59,57,56,54,52,50,48,46,45,43,41,39,37,35,34,32,30,28,26,24,23,21,19,17,15), (1,2,8)(3,7,9)(4,10,5)(6,12,11)(13,43,91)(14,96,37)(15,110,23)(16,90,41)(17,57,73)(18,63,67)(19,20,109)(21,32,95)(22,46,79)(24,59,64)(25,120,112)(26,115,116)(27,34,87)(28,58,61)(29,38,80)(30,35,82)(31,69,47)(33,50,65)(36,60,51)(39,121,98)(40,103,114)(42,52,54)(44,92,122)(45,119,94)(48,101,108)(53,100,105)(55,97,106)(56,89,113)(62,78,118)(66,104,88)(68,72,117)(70,85,102)(71,76,111)(74,77,107)(75,99,84)(81,83,93) ]", "PSL(2,121)^1" ],
  [    887040, "[ (6,12)(7,20)(8,11)(9,22)(13,14)(15,17)(16,19), (1,21)(2,10,8,6)(3,13,4,17)(5,19,9,18)(11,22)(12,14,16,20), (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22) ]", "M22^1" ],
  [    912576, "[ (3,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,51)(3,17,85)(4,43,58)(5,88,12)(6,38,61)(7,89,9)(8,27,70)(10,62,33)(11,20,74)(13,95,93)(14,97,90)(15,25,65)(16,42,47)(18,63,24)(19,56,30)(21,48,36)(22,52,31)(23,29,53)(26,34,45)(28,82,91)(32,75,94)(37,77,87)(39,84,78)(40,92,69)(41,64,96)(44,59,98)(46,83,72)(49,73,79)(50,80,71)(54,81,66)(55,60,86)(57,68,76) ]", "PSL(2,97)^1" ],
  [    976500, "[ (3,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,5,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8)(4,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,126,124,122,120,118,116,114,112,110,108,106,104,102,100,98,6,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38), (1,2,5)(3,4,6)(7,94,38)(8,118,13)(9,57,73)(10,103,26)(11,82,46)(12,52,75)(14,91,35)(15,125,120)(16,83,40)(17,68,54)(18,100,21)(19,97,23)(20,34,86)(22,43,74)(24,85,31)(25,62,53)(27,45,67)(28,63,49)(29,56,55)(30,123,107)(32,64,44)(33,115,112)(36,114,110)(37,41,61)(39,126,95)(42,119,98)(47,99,113)(48,109,102)(50,117,93)(51,122,87)(58,81,121)(59,90,111)(60,76,124)(65,116,79)(66,88,106)(69,101,89)(70,105,84)(71,108,80)(72,92,96)(77,104,78) ]", "PSL(2,125)^1" ],
  [    979200, "[ (7,8,9)(10,14,18)(11,16,21)(12,17,19)(13,15,20)(23,24,25)(26,30,34)(27,32,37)(28,33,35)(29,31,36)(39,40,41)(42,46,50)(43,48,53)(44,49,51)(45,47,52)(55,56,57)(58,62,66)(59,64,69)(60,65,67)(61,63,68)(71,72,73)(74,78,82)(75,80,85)(76,81,83)(77,79,84)(86,115,110)(88,111,122)(89,107,118)(90,119,114)(91,97,150)(92,160,130)(93,142,95)(94,137,170)(96,164,126)(98,133,158)(99,105,146)(100,156,138)(101,154,103)(102,129,166)(104,168,134)(106,125,162)(108,116,112)(109,117,121)(123,136,145)(124,141,135)(127,132,153)(128,149,131)(140,159,157)(144,167,165)(148,163,169)(152,155,161), (1,6,22,42,3)(2,7,38,10,39)(4,8,54,62,49)(5,9,70,82,52)(11,23,26,27,43)(12,71,34,61,48)(13,55,30,76,53)(14,56,46,17,40)(15,72,66,79,51)(16,24,74,37,45)(18,73,50,20,41)(19,57,78,67,47)(21,25,58,32,44)(28,59,64,65,33)(29,75,85,84,36)(31,60,80,83,68)(35,77,69,63,81)(86,166,94,96,138)(87,157,121,112,128)(88,90,167,154,123)(89,160,136,165,133)(91,124,169,95,110)(92,111,119,98,146)(93,153,152,97,103)(99,139,137,164,147)(100,102,120,151,113)(101,129,170,126,156)(104,148,122,125,159)(105,117,135,163,116)(106,131,168,114,141)(107,134,155,127,162)(108,118,109,150,142)(115,144,132,161,145)(130,158,140,143,149) ]", "PSp(4,4)^1" ],
  [   1024128, "[ (3,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,128,126,124,122,120,118,116,114,112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,66)(3,120,12)(4,48,83)(5,33,97)(6,59,70)(7,40,88)(8,96,31)(9,21,105)(10,79,46)(11,67,57)(13,42,80)(14,91,30)(15,22,98)(16,19,100)(17,71,47)(18,23,94)(20,78,37)(24,55,56)(25,50,60)(26,58,51)(27,111,123)(28,68,39)(29,43,63)(32,113,116)(34,110,117)(35,99,127)(36,124,101)(38,109,114)(41,118,102)(44,92,125)(49,84,128)(52,90,119)(53,122,86)(54,112,95)(61,115,85)(62,73,126)(64,104,93)(65,121,75)(69,89,103)(72,82,107)(74,106,81)(76,77,108) ]", "PSL(2,127)^1" ],
  [   1030200, "[ (3,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,53)(3,52,54)(4,84,21)(5,29,75)(6,15,88)(7,23,79)(8,71,30)(9,63,37)(10,42,57)(11,16,82)(12,50,47)(13,60,36)(14,62,33)(17,67,25)(18,91,100)(19,32,58)(20,55,34)(22,102,85)(24,90,95)(26,45,38)(27,83,99)(28,40,41)(31,77,101)(35,98,76)(39,89,81)(43,97,69)(44,92,73)(46,93,70)(48,74,87)(49,64,96)(51,86,72)(56,94,59)(61,80,68)(65,66,78) ]", "PSL(2,101)^1" ],
  [   1036800, "[ (1,13,9,19,3,16,10,21)(2,17,12,22,6,14,7,20,5,18,11,24,4,15,8,23), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (13,14,15,16,17)(20,22,23,21,24) ]", "A6^2" ],
  [   1036800, "[ (1,13,9,19,3,16,10,21)(2,17,12,22,6,14,7,20,5,18,11,24,4,15,8,23), (13,19,15,22,17,23,14,21)(16,20,18,24), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (16,17,18)(19,24,22)(20,23,21) ]", "A6^2" ],
  [   1036800, "[ (1,13,9,19,3,16,10,21)(2,17,12,22,6,14,7,20,5,18,11,24,4,15,8,23), (5,6)(7,9)(8,10)(11,12)(13,21)(14,19,15,20,17,24,16,22,18,23), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (13,14,15,16,17)(20,22,23,21,24) ]", "A6^2" ],
  [   1036800, "[ (1,13,9,21)(2,18,11,23)(3,16,10,19)(4,15,8,24)(5,17,12,20)(6,14,7,22), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (16,17,18)(19,24,22)(20,23,21) ]", "A6^2" ],
  [   1036800, "[ (1,13,9,21)(2,18,11,23)(3,16,10,19)(4,15,8,24)(5,17,12,20)(6,14,7,22), (13,21)(14,19,15,20,17,24,16,22,18,23), (1,9)(2,7,3,8,5,12,4,10,6,11)(13,21)(14,19,15,20,17,24,16,22,18,23), (2,5,3)(7,8,10)(9,11,12) ]", "A6^2" ],
  [   1036800, "[ (1,13,9,21)(2,18,11,23)(3,16,10,19)(4,15,8,24)(5,17,12,20)(6,14,7,22), (5,6)(7,9)(8,10)(11,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (1,9)(2,7,3,8,5,12,4,10,6,11)(13,21)(14,19,15,20,17,24,16,22,18,23), (1,6,4,3,2)(7,12,8,10,11) ]", "A6^2" ],
  [   1036800, "[ (1,19,3,20,5,24,4,22,6,21)(2,23)(7,18,11,16,10,13,9,15,8,14)(12,17), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (16,17,18)(19,24,22)(20,23,21) ]", "A6^2" ],
  [   1036800, "[ (1,21)(2,24,4,20,5,23)(3,22,6,19)(7,17,12,18,11,16,10,13,9,15,8,14), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,19,15,22,17,23,14,21)(16,20,18,24), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (13,14,15,16,17)(20,22,23,21,24) ]", "A6^2" ],
  [   1036800, "[ (1,21)(2,24,4,20,5,23)(3,22,6,19)(7,17,12,18,11,16,10,13,9,15,8,14), (1,7,3,10,5,11,2,9)(4,8,6,12)(13,21)(14,19,15,20,17,24,16,22,18,23), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (2,5,3)(7,8,10)(9,11,12) ]", "A6^2" ],
  [   1036800, "[ (1,21)(2,24,4,20,5,23)(3,22,6,19)(7,17,12,18,11,16,10,13,9,15,8,14), (17,18)(19,21)(20,22)(23,24), (5,6)(7,9)(8,10)(11,12)(17,18)(19,21)(20,22)(23,24), (2,5,3)(7,8,10)(9,11,12) ]", "A6^2" ],
  [   1062720, "[ (3,82,79,71,4,46,43,35)(5,37,16,26,8,73,52,62)(6,64,25,53,9,28,61,17)(7,19,34,80,10,55,70,44)(11,12,15,23,47,48,51,59)(13,18,31,72,49,54,67,36)(14,20,39,24,50,56,75,60)(21,42,32,74,57,78,68,38)(22,45,40,27,58,81,76,63)(29,66,33,77,65,30,69,41), (11,19)(12,27)(13,35)(14,43)(15,51)(16,59)(17,67)(18,75)(20,28)(21,36)(22,44)(23,52)(24,60)(25,68)(26,76)(29,37)(30,45)(31,53)(32,61)(33,69)(34,77)(38,46)(39,54)(40,62)(41,70)(42,78)(47,55)(48,63)(49,71)(50,79)(56,64)(57,72)(58,80)(65,73)(66,81)(74,82), (3,81,79,77,75,10,72,70,68,66,9,63,61,59,57,8,54,52,50,48,4,45,43,41,39,7,36,34,32,30,6,27,25,23,21,5,18,16,14,12)(11,82,80,78,76,74,73,71,69,67,65,64,62,60,58,56,55,53,51,49,47,46,44,42,40,38,37,35,33,31,29,28,26,24,22,20,19,17,15,13), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [   1062720, "[ (3,82,81,80,79,78,77,76,75,74,10,73,72,71,70,69,68,67,66,65,9,64,63,62,61,60,59,58,57,56,8,55,54,53,52,51,50,49,48,47,4,46,45,44,43,42,41,40,39,38,7,37,36,35,34,33,32,31,30,29,6,28,27,26,25,24,23,22,21,20,5,19,18,17,16,15,14,13,12,11), (11,19)(12,27)(13,35)(14,43)(15,51)(16,59)(17,67)(18,75)(20,28)(21,36)(22,44)(23,52)(24,60)(25,68)(26,76)(29,37)(30,45)(31,53)(32,61)(33,69)(34,77)(38,46)(39,54)(40,62)(41,70)(42,78)(47,55)(48,63)(49,71)(50,79)(56,64)(57,72)(58,80)(65,73)(66,81)(74,82), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [   1062720, "[ (5,7)(6,9)(8,10)(11,13,19,35)(12,16,27,59)(14,21,43,36)(15,24,51,60)(17,29,67,37)(18,32,75,61)(20,40,28,62)(22,46,44,38)(23,48,52,63)(25,54,68,39)(26,56,76,64)(30,70,45,41)(31,73,53,65)(33,78,69,42)(34,81,77,66)(47,49,55,71)(50,57,79,72)(58,82,80,74), (11,19)(12,27)(13,35)(14,43)(15,51)(16,59)(17,67)(18,75)(20,28)(21,36)(22,44)(23,52)(24,60)(25,68)(26,76)(29,37)(30,45)(31,53)(32,61)(33,69)(34,77)(38,46)(39,54)(40,62)(41,70)(42,78)(47,55)(48,63)(49,71)(50,79)(56,64)(57,72)(58,80)(65,73)(66,81)(74,82), (3,81,79,77,75,10,72,70,68,66,9,63,61,59,57,8,54,52,50,48,4,45,43,41,39,7,36,34,32,30,6,27,25,23,21,5,18,16,14,12)(11,82,80,78,76,74,73,71,69,67,65,64,62,60,58,56,55,53,51,49,47,46,44,42,40,38,37,35,33,31,29,28,26,24,22,20,19,17,15,13), (1,2,4)(5,6,8)(7,9,10)(11,21,71)(12,66,25)(13,43,47)(14,55,35)(15,37,52)(16,34,54)(17,63,24)(18,20,65)(19,36,49)(22,72,82)(23,51,29)(26,33,45)(27,81,68)(28,73,75)(30,76,69)(31,32,40)(38,79,58)(39,59,77)(41,56,78)(42,70,64)(44,57,74)(46,50,80)(48,60,67)(53,61,62) ]", "PSL(2,81)^1" ],
  [   1092624, "[ (3,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,54)(3,10,98)(4,73,34)(5,40,66)(6,30,75)(7,24,80)(8,92,11)(9,21,81)(12,23,76)(13,60,38)(14,46,51)(15,49,47)(16,100,97)(17,39,55)(18,64,29)(19,56,36)(20,26,65)(22,31,58)(25,45,41)(27,87,99)(28,84,101)(32,85,96)(33,78,102)(35,104,74)(42,68,103)(43,82,88)(44,90,79)(48,95,70)(50,77,86)(52,89,72)(53,69,91)(57,62,94)(59,93,61)(63,83,67) ]", "PSL(2,103)^1" ],
  [   1123980, "[ (3,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)(4,132,130,128,126,124,122,120,118,116,114,112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6), (1,2,68)(3,67,69)(4,126,9)(5,22,112)(6,54,79)(7,25,107)(8,70,61)(10,132,127)(11,87,41)(12,77,50)(13,110,16)(14,28,97)(15,52,72)(17,21,101)(18,33,88)(19,27,93)(20,81,38)(23,42,74)(24,114,131)(26,123,120)(29,111,129)(30,58,51)(31,71,37)(32,63,44)(34,60,45)(35,115,119)(36,47,56)(39,108,122)(40,46,53)(43,109,117)(48,103,118)(49,125,95)(55,116,98)(57,82,130)(59,124,86)(62,94,113)(64,84,121)(65,105,99)(66,128,75)(73,104,92)(76,102,91)(78,106,85)(80,89,100)(83,90,96) ]", "PSL(2,131)^1" ],
  [   1209600, "[ (5,72)(7,37)(9,64)(10,65)(11,30)(12,34)(13,24)(14,46)(15,48)(16,35)(17,75)(18,56)(20,98)(21,52)(22,89)(23,39)(26,50)(27,85)(28,43)(29,92)(32,96)(33,71)(36,44)(38,93)(40,90)(41,79)(42,51)(45,55)(49,84)(53,97)(57,78)(58,88)(59,81)(61,83)(62,76)(63,100)(66,74)(68,70)(69,77)(73,87)(82,86)(91,99)(94,95), (1,58,96,14,36,4,25,71)(2,20,85,42,50,92,64,31)(3,51,5,17,89,34,99,11)(6,70)(7,90,12,19,82,86,54,23)(8,43,37,57,77,75,30,73)(9,52,53,95)(10,59,91,28,97,32,68,40)(13,56,74,78,80,46,38,21)(15,100,63,41,27,67,22,35)(16,69,83,24)(18,33,45,81,55,29,98,60)(26,72,47,62)(39,76)(44,79,94,65,88,61,66,49)(48,84) ]", "J_2^1" ],
  [   1224936, "[ (3,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4), (1,2,56)(3,55,57)(4,92,19)(5,9,101)(6,22,87)(7,27,81)(8,70,37)(10,33,72)(11,103,107)(12,86,17)(13,28,74)(14,52,49)(15,29,71)(16,46,53)(18,58,39)(20,108,93)(21,62,32)(23,47,45)(24,43,48)(25,90,106)(26,100,95)(30,51,34)(31,85,105)(35,44,36)(38,84,99)(40,79,102)(41,83,97)(42,104,75)(50,91,80)(54,94,73)(59,66,96)(60,98,63)(61,82,78)(64,69,88)(65,89,67)(68,77,76) ]", "PSL(2,107)^1" ],
--> --------------------

--> maximum size reached

--> --------------------

Quelle targetsQuotient.gi Sprache: unbekannt

[ Dauer der Verarbeitung: 0.18 Sekunden (vorverarbeitet) ]