direct product, non-abelian, not soluble, A-group
Aliases: C7×A5, SmallGroup(420,13)
Series: Chief►Derived ►Lower central ►Upper central
| A5 — C7×A5 |
| A5 — C7×A5 |
Smallest permutation representation of C7×A5
►On 35 points
Generators in S35
(1 9 17 11 19 27 21 29 2 31 4 12 6 14 22 16 24 32 26 34 7)(3 18 33 13 28 8 23)(5 20 35 15 30 10 25)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35)
G:=sub<Sym(35)| (1,9,17,11,19,27,21,29,2,31,4,12,6,14,22,16,24,32,26,34,7)(3,18,33,13,28,8,23)(5,20,35,15,30,10,25), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35)>;
G:=Group( (1,9,17,11,19,27,21,29,2,31,4,12,6,14,22,16,24,32,26,34,7)(3,18,33,13,28,8,23)(5,20,35,15,30,10,25), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35) );
G=PermutationGroup([[(1,9,17,11,19,27,21,29,2,31,4,12,6,14,22,16,24,32,26,34,7),(3,18,33,13,28,8,23),(5,20,35,15,30,10,25)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35)]])
35 conjugacy classes
| class | 1 | 2 | 3 | 5A | 5B | 7A | ··· | 7F | 14A | ··· | 14F | 21A | ··· | 21F | 35A | ··· | 35L |
| order | 1 | 2 | 3 | 5 | 5 | 7 | ··· | 7 | 14 | ··· | 14 | 21 | ··· | 21 | 35 | ··· | 35 |
| size | 1 | 15 | 20 | 12 | 12 | 1 | ··· | 1 | 15 | ··· | 15 | 20 | ··· | 20 | 12 | ··· | 12 |
35 irreducible representations
| dim | 1 | 1 | 3 | 3 | 4 | 4 | 5 | 5 |
| type | + | + | + | + | ||||
| image | C1 | C7 | A5 | C7×A5 | A5 | C7×A5 | A5 | C7×A5 |
| kernel | C7×A5 | A5 | C7 | C1 | C7 | C1 | C7 | C1 |
| # reps | 1 | 6 | 2 | 12 | 1 | 6 | 1 | 6 |
Matrix representation of C7×A5 ►in GL3(𝔽211) generated by
| 109 | 63 | 57 |
| 102 | 0 | 183 |
| 49 | 0 | 102 |
| 80 | 29 | 87 |
| 37 | 2 | 148 |
| 132 | 128 | 35 |
G:=sub<GL(3,GF(211))| [109,102,49,63,0,0,57,183,102],[80,37,132,29,2,128,87,148,35] >;
C7×A5 in GAP, Magma, Sage, TeX
C_7\times A_5
% in TeX
G:=Group("C7xA5"); // GroupNames label
G:=SmallGroup(420,13);
// by ID
G=gap.SmallGroup(420,13);
# by ID
Export