bad0@trit1:~$ magma
Magma V2.19-9 Wed Oct 7 2015 12:45:31 on trit1 [Seed = 1107384403]
+-------------------------------------------------------------------+
| This copy of Magma has been made available through a |
| generous initiative of the |
| |
| Simons Foundation |
| |
| covering U.S. Colleges, Universities, Nonprofit Research entities,|
| and their students, faculty, and staff |
+-------------------------------------------------------------------+
Type ? for help. Type -D to quit.
#exceptional case Alt(8) non-isomorphic to L(3,4), both order 20160
# = (2^6)(3^2)*(5*7)
> C1:=ATLASGroup("A8");
> mrkC1:=MatRepKeys(C1);
> mrkC1;
[
Matrix rep of degree 4 over GF(2) named a,
Matrix rep of degree 4 over GF(2) named b,
Matrix rep of degree 6 over GF(2),
Matrix rep of degree 14 over GF(2),
Matrix rep of degree 20 over GF(2) named a,
Matrix rep of degree 20 over GF(2) named b,
Matrix rep of degree 64 over GF(2)
]
> PermRepKeys(C1);
[
Perm rep of degree 8,
Perm rep of degree 15 named a,
Perm rep of degree 15 named b
]
> C2:=ATLASGroup("L34");
> mrkC2:=MatRepKeys(C2);
> mrkC2;
[
Matrix rep of degree 9 over GF(2) named a,
Matrix rep of degree 9 over GF(2) named b,
Matrix rep of degree 16 over GF(2),
Matrix rep of degree 64 over GF(2),
Matrix rep of degree 8 over GF(4) named a,
Matrix rep of degree 8 over GF(4) named b,
Matrix rep of degree 15 over GF(3) named a,
Matrix rep of degree 15 over GF(3) named b,
Matrix rep of degree 15 over GF(3) named c,
Matrix rep of degree 19 over GF(3),
Matrix rep of degree 90 over GF(3),
Matrix rep of degree 126 over GF(3),
Matrix rep of degree 45 over GF(9) named a,
Matrix rep of degree 45 over GF(9) named b,
Matrix rep of degree 63 over GF(9) named a,
Matrix rep of degree 63 over GF(9) named b,
Matrix rep of degree 20 over GF(5),
Matrix rep of degree 35 over GF(5) named a,
Matrix rep of degree 35 over GF(5) named b,
Matrix rep of degree 35 over GF(5) named c,
Matrix rep of degree 63 over GF(5),
Matrix rep of degree 90 over GF(5),
Matrix rep of degree 45 over GF(25) named a,
Matrix rep of degree 45 over GF(25) named b,
Matrix rep of degree 19 over GF(7),
Matrix rep of degree 35 over GF(7) named a,
Matrix rep of degree 35 over GF(7) named b,
Matrix rep of degree 35 over GF(7) named c,
Matrix rep of degree 45 over GF(7),
Matrix rep of degree 126 over GF(7),
Matrix rep of degree 63 over GF(49) named a,
Matrix rep of degree 63 over GF(49) named b
]
> PermRepKeys(C2);
[
Perm rep of degree 21 named a,
Perm rep of degree 21 named b,
Perm rep of degree 56 named a,
Perm rep of degree 56 named b,
Perm rep of degree 56 named c,
Perm rep of degree 120 named a,
Perm rep of degree 120 named b,
Perm rep of degree 120 named c,
Perm rep of degree 280
]
--------------------------------------
> A:=ATLASGroup("O73");
> PermRepKeys(A);
[
Perm rep of degree 351,
Perm rep of degree 364,
Perm rep of degree 378,
Perm rep of degree 1080 named a,
Perm rep of degree 1080 named b,
Perm rep of degree 1120,
Perm rep of degree 3640
]
> MatRepKeys(A);
[
Matrix rep of degree 78 over GF(2),
Matrix rep of degree 90 over GF(2),
Matrix rep of degree 104 over GF(2),
Matrix rep of degree 260 over GF(2) named a,
Matrix rep of degree 260 over GF(2) named b,
Matrix rep of degree 7 over GF(3),
Matrix rep of degree 21 over GF(3),
Matrix rep of degree 27 over GF(3),
Matrix rep of degree 35 over GF(3),
Matrix rep of degree 63 over GF(3),
Matrix rep of degree 189 over GF(3) named a,
Matrix rep of degree 309 over GF(3),
Matrix rep of degree 78 over GF(5),
Matrix rep of degree 78 over GF(7),
Matrix rep of degree 78 over GF(13)
]
> prk:=PermRepKeys(A);
> prk;
[
Perm rep of degree 351,
Perm rep of degree 364,
Perm rep of degree 378,
Perm rep of degree 1080 named a,
Perm rep of degree 1080 named b,
Perm rep of degree 1120,
Perm rep of degree 3640
]
> K:=prk[1];
> G:=PermutationGroup(K);
------------
> B:=ATLASGroup("S63");
> B:=ATLASGroup("S63");
> mrkB:=MatRepKeys(B);
> mrkB;
[
Matrix rep of degree 78 over GF(2),
Matrix rep of degree 13 over GF(4) named a,
Matrix rep of degree 13 over GF(25) named a,
Matrix rep of degree 13 over GF(7) named a
]
> PermRepKeys(B);
[
Perm rep of degree 364,
Perm rep of degree 1120,
Perm rep of degree 3640,
Perm rep of degree 7371
]
> #Both groups simple of order 4,585,351,680 = (2^9)(3^9)x(5*7*13).