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AtlasRep Info for L₃(2)

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Representations for G = L₃(2): (all refer to std. generators 1)

1	G ≤ Sym(7a)	2-trans., on cosets of S4 (1st max.)
2	G ≤ Sym(7b)	2-trans., on cosets of S4 (2nd max.)
3	G ≤ Sym(8)	2-trans., on cosets of 7:3 (3rd max.)
4	G ≤ Sym(14a)	rank 3, on cosets of A4 < S4
5	G ≤ Sym(14b)	rank 3, on cosets of A4 < S4
6	G ≤ Sym(21)	rank 6, on cosets of D8 < S4
7	G ≤ Sym(24)	rank 6, on cosets of 7 < 7:3
8	G ≤ Sym(28)	rank 7, on cosets of S3 < S4
9	G ≤ Sym(42a)	rank 15, on cosets of 22 < S4
10	G ≤ Sym(42b)	rank 15, on cosets of 22 < S4
11	G ≤ Sym(42c)	rank 12, on cosets of 4 < S4
12	G ≤ Sym(56)	rank 20, on cosets of 3 < S4
13	G ≤ Sym(84)	rank 44, on cosets of 2 < S4
14	G ≤ Sym(168)	rank 168, on cosets of 1 < S4
15	G ≤ GL(3a,2)
16	G ≤ GL(3b,2)
17	G ≤ GL(8,2)
18	G ≤ GL(6a,3)
19	G ≤ GL(6b,3)
20	G ≤ GL(7,3)
21	G ≤ GL(3,7)
22	G ≤ GL(5,7)
23	G ≤ GL(7,7)
24	G ≤ GL(3a,9)
25	G ≤ GL(3b,9)
26	G ≤ GL(6a,ℤ)
27	G ≤ GL(6b,ℤ)
28	G ≤ GL(7,ℤ)
29	G ≤ GL(8,ℤ)
30	G ≤ GL(3a,Field([Sqrt(-7)]))
31	G ≤ GL(3b,Field([Sqrt(-7)]))

Programs for G = L₃(2): (all refer to std. generators 1)

• presentation:
• maxes (all 3):

  1	S4
  1	S4
  1	S4
  2	S4
  2	S4
  2	S4
  3	7:3
  3	7:3
  3	7:3

• std. gen. checker:

  (check)

  (pres)

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