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AtlasRep Info for L₃(4)

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Representations for G = L₃(4): (all refer to std. generators 1)

1	G ≤ Sym(21a)	2-trans., on cosets of 24:A5 (1st max.)
2	G ≤ Sym(21b)	2-trans., on cosets of 24:A5 (2nd max.)
3	G ≤ Sym(56a)	rank 3, on cosets of A6 (3rd max.)
4	G ≤ Sym(56b)	rank 3, on cosets of A6 (4th max.)
5	G ≤ Sym(56c)	rank 3, on cosets of A6 (5th max.)
6	G ≤ Sym(120a)	rank 4, on cosets of L3(2) (6th max.)
7	G ≤ Sym(120b)	rank 4, on cosets of L3(2) (7th max.)
8	G ≤ Sym(120c)	rank 4, on cosets of L3(2) (8th max.)
9	G ≤ Sym(280)	rank 8, on cosets of 32:Q8 (9th max.)
10	G ≤ GL(9a,2)
11	G ≤ GL(9b,2)
12	G ≤ GL(16,2)
13	G ≤ GL(64,2)
14	G ≤ GL(15a,3)
15	G ≤ GL(15b,3)
16	G ≤ GL(15c,3)
17	G ≤ GL(19,3)
18	G ≤ GL(90,3)
19	G ≤ GL(126,3)
20	G ≤ GL(8a,4)
21	G ≤ GL(8b,4)
22	G ≤ GL(20,5)
23	G ≤ GL(35a,5)
24	G ≤ GL(35b,5)
25	G ≤ GL(35c,5)
26	G ≤ GL(63,5)
27	G ≤ GL(90,5)
28	G ≤ GL(19,7)
29	G ≤ GL(35a,7)
30	G ≤ GL(35b,7)
31	G ≤ GL(35c,7)
32	G ≤ GL(45,7)
33	G ≤ GL(126,7)
34	G ≤ GL(45a,9)
35	G ≤ GL(45b,9)
36	G ≤ GL(63a,9)
37	G ≤ GL(63b,9)
38	G ≤ GL(45a,25)
39	G ≤ GL(45b,25)
40	G ≤ GL(63a,49)
41	G ≤ GL(63b,49)
42	G ≤ GL(20,ℤ)
43	G ≤ GL(35a,ℤ)
44	G ≤ GL(35b,ℤ)
45	G ≤ GL(35c,ℤ)
46	G ≤ GL(64,ℤ)
47	G ≤ GL(63a,Field([Sqrt(5)]))
48	G ≤ GL(63b,Field([Sqrt(5)]))

Programs for G = L₃(4): (all refer to std. generators 1)

• presentation:
• maxes (7 out of 9):

  1	24:A5
  2	24:A5
  3	A6
  3	A6
  6	L3(2)
  6	L3(2)
  7	L3(2)
  7	L3(2)
  8	L3(2)
  8	L3(2)
  9	32:Q8

• standardizations of maxes:

  from 6th max., version 1 to L3(2), std. 1

  from 7th max., version 1 to L3(2), std. 1

  from 8th max., version 1 to L3(2), std. 1

• std. gen. checker:

  (check)

  (pres)

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