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AtlasRep Info for 3.A₇

→ ATLAS page for 3.A₇

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Representations for G = 3.A₇: (all refer to std. generators 1)

1	G ≤ Sym(45a)	rank 4, on cosets of L2(7) < 3 × L2(7)
2	G ≤ Sym(45b)	rank 4, on cosets of L2(7) < 3 × L2(7)
3	G ≤ Sym(63)	rank 7, on cosets of S5 < 3 × S5
4	G ≤ Sym(315)	rank 28, on cosets of S4 < 3.A6
5	G ≤ GL(12,2)
6	G ≤ GL(30,2)
7	G ≤ GL(48a,2)
8	G ≤ GL(48b,2)
9	G ≤ GL(6,4)
10	G ≤ GL(15,4)
11	G ≤ GL(24a,4)
12	G ≤ GL(24b,4)
13	G ≤ GL(6,5)
14	G ≤ GL(12,5)
15	G ≤ GL(30a,5)
16	G ≤ GL(30b,5)
17	G ≤ GL(36,5)
18	G ≤ GL(42,5)
19	G ≤ GL(6,7)
20	G ≤ GL(9,7)
21	G ≤ GL(15,7)
22	G ≤ GL(21a,7)
23	G ≤ GL(21b,7)
24	G ≤ GL(3,25)
25	G ≤ GL(6,25)
26	G ≤ GL(15a,25)
27	G ≤ GL(15b,25)
28	G ≤ GL(18,25)
29	G ≤ GL(21,25)
30	G ≤ GL(6,Field([Sqrt(-3)]))
31	G ≤ GL(15a,Field([Sqrt(-3)]))
32	G ≤ GL(15b,Field([Sqrt(-3)]))
33	G ≤ GL(21a,Field([Sqrt(-3)]))
34	G ≤ GL(21b,Field([Sqrt(-3)]))

Programs for G = 3.A₇:

• maxes (2 out of 5):

  1	3.A6
  2	3 × L3(2)

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