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AtlasRep Info for O₈⁺(3)

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Representations for G = O₈⁺(3): (all refer to std. generators 1)

1	G ≤ Sym(1080a)	rank 3, on cosets of O7(3) (1st max.)
2	G ≤ Sym(1080b)	rank 3, on cosets of O7(3) (2nd max.)
3	G ≤ Sym(1080c)	rank 3, on cosets of O7(3) (3rd max.)
4	G ≤ Sym(1080d)	rank 3, on cosets of O7(3) (4th max.)
5	G ≤ Sym(1080e)	rank 3, on cosets of O7(3) (5th max.)
6	G ≤ Sym(1080f)	rank 3, on cosets of O7(3) (6th max.)
7	G ≤ Sym(1120a)	rank 3, on cosets of 36:L4(3) (7th max.)
8	G ≤ Sym(1120b)	rank 3, on cosets of 36:L4(3) (8th max.)
9	G ≤ Sym(1120c)	rank 3, on cosets of 36:L4(3) (9th max.)
10	G ≤ Sym(28431a)	rank 6, on cosets of O8+(2) (10th max.)
11	G ≤ Sym(28431b)	rank 6, on cosets of O8+(2) (11th max.)
12	G ≤ Sym(28431c)	rank 6, on cosets of O8+(2) (12th max.)
13	G ≤ Sym(28431d)	rank 6, on cosets of O8+(2) (13th max.)
14	G ≤ Sym(36400)	rank 7, on cosets of 31+8+:2(A4 × A4 × A4).2 (14th max.)
15	G ≤ GL(298,2)
16	G ≤ GL(28,3)
17	G ≤ GL(35a,3)
18	G ≤ GL(35b,3)
19	G ≤ GL(35c,3)
20	G ≤ GL(195,3)
21	G ≤ GL(322,3)
22	G ≤ GL(518a,3)
23	G ≤ GL(518b,3)
24	G ≤ GL(518c,3)
25	G ≤ GL(567a,3)
26	G ≤ GL(567b,3)
27	G ≤ GL(567c,3)
28	G ≤ GL(300,5)
29	G ≤ GL(299,7)
30	G ≤ GL(300,13)

Programs for G = O₈⁺(3): (all refer to std. generators 1)

• maxes (7 out of 27):

  1	O7(3)
  2	O7(3)
  7	36:L4(3)
  10	O8+(2)
  11	O8+(2)
  12	O8+(2)
  13	O8+(2)

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