Aliases: C8.A5, SL2(𝔽5).C4, C4.5(C2×A5), C2.2(C4×A5), C4.A5.3C2, SmallGroup(480,221)
Series: Chief►Derived ►Lower central ►Upper central
| SL2(𝔽5) — C8.A5 |
| SL2(𝔽5) — C8.A5 |
30C2
10C3
6C5
15C22
15C4
10S3
10S3
10C6
6D5
6C10
6D5
5Q8
15D4
15C8
15C2×C4
10C12
10Dic3
10D6
6C20
6Dic5
6D10
15C2×C8
15M4(2)
10C4×S3
10C3⋊C8
10C24
6C40
10S3×C8
Smallest permutation representation of C8.A5
►On 48 points
Generators in S48
(1 40 34 3 10 44 5 20 14 7 30 24)(2 25 19 4 35 29 6 45 39 8 15 9)(11 27 23 21 37 33 31 47 43 41 17 13)(12 48 46 22 18 16 32 28 26 42 38 36)
(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 36 37 38 39 40 41 42 43 44 45 46 47 48)
G:=sub<Sym(48)| (1,40,34,3,10,44,5,20,14,7,30,24)(2,25,19,4,35,29,6,45,39,8,15,9)(11,27,23,21,37,33,31,47,43,41,17,13)(12,48,46,22,18,16,32,28,26,42,38,36), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)>;
G:=Group( (1,40,34,3,10,44,5,20,14,7,30,24)(2,25,19,4,35,29,6,45,39,8,15,9)(11,27,23,21,37,33,31,47,43,41,17,13)(12,48,46,22,18,16,32,28,26,42,38,36), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48) );
G=PermutationGroup([[(1,40,34,3,10,44,5,20,14,7,30,24),(2,25,19,4,35,29,6,45,39,8,15,9),(11,27,23,21,37,33,31,47,43,41,17,13),(12,48,46,22,18,16,32,28,26,42,38,36)], [(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)]])
36 conjugacy classes
| class | 1 | 2A | 2B | 3 | 4A | 4B | 4C | 5A | 5B | 6 | 8A | 8B | 8C | 8D | 8E | 8F | 10A | 10B | 12A | 12B | 20A | 20B | 20C | 20D | 24A | 24B | 24C | 24D | 40A | ··· | 40H |
| order | 1 | 2 | 2 | 3 | 4 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 8 | 8 | 8 | 8 | 10 | 10 | 12 | 12 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 40 | ··· | 40 |
| size | 1 | 1 | 30 | 20 | 1 | 1 | 30 | 12 | 12 | 20 | 1 | 1 | 1 | 1 | 30 | 30 | 12 | 12 | 20 | 20 | 12 | 12 | 12 | 12 | 20 | 20 | 20 | 20 | 12 | ··· | 12 |
36 irreducible representations
| dim | 1 | 1 | 1 | 2 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 6 |
| type | + | + | + | + | + | + | + | + | |||||||
| image | C1 | C2 | C4 | C8.A5 | A5 | C2×A5 | C4×A5 | A5 | C2×A5 | C4×A5 | C8.A5 | A5 | C2×A5 | C4×A5 | C8.A5 |
| kernel | C8.A5 | C4.A5 | SL2(𝔽5) | C1 | C8 | C4 | C2 | C8 | C4 | C2 | C1 | C8 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 8 | 2 | 2 | 4 | 1 | 1 | 2 | 4 | 1 | 1 | 2 | 4 |
Matrix representation of C8.A5 ►in GL2(𝔽41) generated by
| 30 | 32 |
| 16 | 2 |
| 22 | 13 |
| 31 | 3 |
G:=sub<GL(2,GF(41))| [30,16,32,2],[22,31,13,3] >;
C8.A5 in GAP, Magma, Sage, TeX
C_8.A_5
% in TeX
G:=Group("C8.A5"); // GroupNames label
G:=SmallGroup(480,221);
// by ID
G=gap.SmallGroup(480,221);
# by ID
Export