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AtlasRep Info for S₆(3)

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Representations for G = S₆(3): (all refer to std. generators 1)

1	G ≤ Sym(364)	rank 3, on cosets of 31+4+.2U4(2) (1st max.)
2	G ≤ Sym(1120)	rank 4, on cosets of 36:L3(3) (2nd max.)
3	G ≤ Sym(3640)	rank 5, on cosets of 33+4:2(S4 × A4) (3rd max.)
4	G ≤ Sym(7371)	rank 6, on cosets of 2.(A4 × U4(2)) (4th max.)
5	G ≤ GL(78,2)
6	G ≤ GL(13a,4)
7	G ≤ GL(13a,7)
8	G ≤ GL(13a,25)
9	G ≤ GL(105,ℤ)
10	G ≤ GL(168,ℤ)
11	G ≤ GL(195,ℤ)
12	G ≤ GL(13a,Field([Sqrt(-3)]))
13	G ≤ GL(13b,Field([Sqrt(-3)]))
14	G ≤ GL(78,Field([Sqrt(-3)]))
15	G ≤ GL(91a,Field([Sqrt(-3)]))
16	G ≤ GL(91b,Field([Sqrt(-3)]))

Programs for G = S₆(3): (all refer to std. generators 1)

• maxes (10 out of 11):

  1	31+4+.2U4(2)
  2	36:L3(3)
  4	2.(A4 × U4(2))
  5	22+6:33:S3
  6	L2(27).3
  7	2 × U3(3).2
  8	L3(3).2
  9	L2(13)
  10	L2(13)
  11	A5

File created automatically by GAP on 22-Apr-2022.