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AtlasRep Info for S₈(2)

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Representations for G = S₈(2): (all refer to std. generators 1)

1	G ≤ Sym(120)	2-trans., on cosets of O8−(2).2 (1st max.)
2	G ≤ Sym(136)	2-trans., on cosets of O8+(2).2 (2nd max.)
3	G ≤ Sym(240)	rank 4, on cosets of O8−(2) < O8−(2).2
4	G ≤ Sym(255)	rank 3, on cosets of 27:S6(2) (3rd max.)
5	G ≤ Sym(272)	rank 4, on cosets of O8+(2) < O8+(2).2
6	G ≤ Sym(2295)	rank 5, on cosets of 210:A8 (4th max.)
7	G ≤ Sym(5355)	rank 6, on cosets of 23+8:(S3 × S6) (5th max.)
8	G ≤ GL(8,2)
9	G ≤ GL(16,2)
10	G ≤ GL(26,2)
11	G ≤ GL(48,2)
12	G ≤ GL(35,3)
13	G ≤ GL(50,3)
14	G ≤ GL(35,5)
15	G ≤ GL(51,5)
16	G ≤ GL(35,7)
17	G ≤ GL(51,7)
18	G ≤ GL(35,17)
19	G ≤ GL(51,17)
20	G ≤ GL(35,ℤ)
21	G ≤ GL(51,ℤ)
22	G ≤ GL(85,ℤ)
23	G ≤ GL(119,ℤ)
24	G ≤ GL(135,ℤ)

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