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G = C8.A5order 480 = 25·3·5

The central extension by C8 of A5

non-abelian, not soluble

Aliases: C8.A5, SL2(𝔽5).C4, C4.5(C2×A5), C2.2(C4×A5), C4.A5.3C2, SmallGroup(480,221)

Series: ChiefDerived Lower central Upper central

C1C2C4C8 — C8.A5
SL2(𝔽5) — C8.A5
SL2(𝔽5) — C8.A5
C1C8

30C2
10C3
6C5
15C22
15C4
10S3
10S3
10C6
6D5
6C10
6D5
5Q8
15D4
15C8
15C2×C4
10C12
10Dic3
10D6
6C20
6Dic5
6D10
5C4○D4
15C2×C8
15M4(2)
5SL2(𝔽3)
10C4×S3
10C3⋊C8
10C24
6C52C8
6C40
6C4×D5
5C8○D4
5C4.A4
10S3×C8
6C8×D5
5C8.A4

Smallest permutation representation of C8.A5
On 48 points
Generators in S48
(1 10 44 3 20 14 5 30 24 7 40 34)(2 35 29 4 45 39 6 15 9 8 25 19)(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)| (1,10,44,3,20,14,5,30,24,7,40,34)(2,35,29,4,45,39,6,15,9,8,25,19)(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( (1,10,44,3,20,14,5,30,24,7,40,34)(2,35,29,4,45,39,6,15,9,8,25,19)(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([(1,10,44,3,20,14,5,30,24,7,40,34),(2,35,29,4,45,39,6,15,9,8,25,19),(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 2A2B 3 4A4B4C5A5B 6 8A8B8C8D8E8F10A10B12A12B20A20B20C20D24A24B24C24D40A···40H
order122344455688888810101212202020202424242440···40
size11302011301212201111303012122020121212122020202012···12

36 irreducible representations

dim111233344445556
type++++++++
imageC1C2C4C8.A5A5C2×A5C4×A5A5C2×A5C4×A5C8.A5A5C2×A5C4×A5C8.A5
kernelC8.A5C4.A5SL2(𝔽5)C1C8C4C2C8C4C2C1C8C4C2C1
# reps112822411241124

Matrix representation of C8.A5 in GL2(𝔽41) generated by

3032
162
,
2213
313
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

Subgroup lattice of C8.A5 in TeX

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