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AtlasRep Info for L₃(8)

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Representations for G = L₃(8): (all refer to std. generators 1)

1	G ≤ Sym(73a)	2-trans., on cosets of 26:(7 × L2(8)) (1st max.)
2	G ≤ Sym(73b)	2-trans., on cosets of 26:(7 × L2(8)) (2nd max.)
3	G ≤ Sym(56064)	rank 220, on cosets of 72:S3 (3rd max.)
4	G ≤ Sym(75264)	rank 372, on cosets of 73:3 (4th max.)
5	G ≤ Sym(98112)	rank 653, on cosets of L3(2) (5th max.)
6	G ≤ GL(27,2)	character 27a
7	G ≤ GL(512,2)	character 512a
8	G ≤ GL(72,3)	character 72a
9	G ≤ GL(511,3)	character 511a
10	G ≤ GL(72,7)	character 72a
11	G ≤ GL(511,7)	character 511a
12	G ≤ GL(512,7)	character 512a
13	G ≤ GL(3,8)
14	G ≤ GL(8,8)
15	G ≤ GL(9a,8)
16	G ≤ GL(9b,8)
17	G ≤ GL(24a,8)
18	G ≤ GL(24b,8)
19	G ≤ GL(27,8)
20	G ≤ GL(64,8)
21	G ≤ GL(72a,8)
22	G ≤ GL(72b,8)
23	G ≤ GL(192,8)
24	G ≤ GL(657,27)
25	G ≤ GL(71,73)	character 71a
26	G ≤ GL(441,73)	character 441a
27	G ≤ GL(511a,73)	character 511a
28	G ≤ GL(511b,73)	character 511b
29	G ≤ GL(511,343)	character 511b
30	G ≤ GL(72,ℤ)	character 72a
31	G ≤ GL(73a,Field([E(7)]))
32	G ≤ GL(73b,Field([E(7)]))
33	G ≤ GL(73c,Field([E(7)]))
34	G ≤ GL(73d,Field([E(7)]))
35	G ≤ GL(73e,Field([E(7)]))
36	G ≤ GL(73f,Field([E(7)]))

Programs for G = L₃(8): (all refer to std. generators 1)

• repr. cyc. subg.:
• std. gen. checker:
• automorphisms:

  3

  6

• maxes (all 5):

  1	26:(7 × L2(8))
  2	26:(7 × L2(8))
  3	72:S3
  4	73:3
  5	L3(2)

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