Example 1:
SL(55,9) blown up into GL(110,3)
--> works, but evaluation of nice gens is hard
Example 2:
2.L(3,9).2 in GL(91,5), in between conjugated in GL(91,25)
--> works, Alt/Sym(92) takes some time to fail, what can be done?
Example 3:
Lots of small subspaces, lots of A5s
Seems to be D2, found by D2D4.
Size=25865000878872449940580467214609161388032000000000000000000000000000000000000000000000000
--> works, takes some time to build tree..., needs lots of memory
Example 4:
Contains eventually a classical SL(57,4).
--> works, but evaluation of nice gens is hard
Example 5:
Contains eventually a classical orthogonal group.
--> does not yet work, even fails miserably in FindElmOfEvenNormalSubgroup
Example 6:
Problems with matrices over field GF(2^16).
--> does not yet work, because no compression for such matrices
Example 7:
Comes from something in GL(10,3^10). Currently not feasible due to
proper matrices.
--> does not yet work
Example 8:
HS in a 21-dimension irreducible rep over GF(25), "augmented" to dimension
98 by conjugating it around in GL(98,25).
--> works perfectly, Size=44352000
Example 9:
MeatAxe-Problems over GF(61^2) and many generators!
--> ???, runs very long
Example 10:
Seems to be O+8(5) in a 160-dim irreducible rep in defining
characteristic.
--> does not work yet
Example 11:
Done, Size=2234313234074738601500687771369472
ganz unten 2, L(2,37)'s, oben drauf eine PSL(2,7)
This seems to be tensor induced D7!
Seems to be (SL(2,37)^\otimes 7).L(3,2) (on 7 points)
--> works, involution jumper takes it apart
Example 12:
3^(1+17).U(8,2).3.2
with size: 396361728
--> works?
Challenge 1:
60.M22 over GF(11^2) in dimension 24 but not subfield!
--> works by hinted StabilizerChain
Challenge 2:
J4 over GF(2^2) dim 112, subfield coming from GF(2)
--> does not work because J4 cannot be handled sensibly
Challenge 3:
L2(243) over GF(11^2) in dimension 121
--> works, done by StabilizerChain in the end, do we want to hint at
this?
Challenge 4:
Two largest projective orders: 780, 390 ???
This seems to be D7, found by doing involution trick twice.
--> Works, D247 finds it, size is 615019392000000000000
Challenge 5:
This is C6: 2^(1+8).Omega^+_8(2) < 2^(1+8).Sp(8,2) extraspecial.
--> Works, C6 finds it, then LieType finds it.
Challenge 6:
Has to to something with SL(55,11), but it seems to be smaller!
Maybe a classical group in some bigger representation?
This is L10(11) in a 55-dim rep, special method missing.
(probably adjoint rep?)
--> does not work (yet)
Challenge 7:
Highly reducible group involving 2^{15}.SL(3,2).A5
Size 330301440
--> works perfectly
Challenge 8:
Reducible, contains L(5,13) (done by classical natural)
Size 2952418014702027260072949983477760000.
--> works perfectly
Challenge 9:
Tensor decomposable, S(6,3) and 2.O(7,3) (in dimension 8).
D2D4 does it, then StabilizerChain, although non-constr. recog. is OK
Size 42050900058557644800.
--> works perfectly
Challenge 10:
Size 4751625928405674992410967408640000000000000000000000000
This seems to be S.5 wr M24 with S5's irred. rep in dim 4
--> works perfectly, although slowly
Challenge 11:
This is SL(80,71).
--> works perfectly, preimages of nice generators always problematic
here also kernel gens and sifting
Challenge 12:
Size is 8412055600858398720, this is 2^35.M24.
Imprimitive D2, D247 finds it readily.
--> works perfectly
Challenge 13:
Imprimitive, 21 blocks, L2(7) acting on top, below are 7 copies of
L2(7), size is 649791775986809831424.
--> works perfectly
Challenge 14:
This is SL(8,251) tensor SL(9,251) (tensor decomposable D4).
--> works perfectly
Challenge 15:
SL(5,625) blown up to GL(20,5), is recognised but then
classicalnatural does not work because field GF(625) not compressed.
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