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G = C96order 96 = 25·3

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C96, also denoted Z96, SmallGroup(96,2)

Series: Derived Chief Lower central Upper central

C1 — C96
C1C2C4C8C16C48 — C96
C1 — C96
C1 — C96

Generators and relations for C96
 G = < a | a96=1 >


Smallest permutation representation of C96
Regular action on 96 points
Generators in S96
(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 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96)

G:=sub<Sym(96)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)])

C96 is a maximal subgroup of   C3⋊C64  C96⋊C2  D96  C32⋊S3  Dic48

96 conjugacy classes

class 1  2 3A3B4A4B6A6B8A8B8C8D12A12B12C12D16A···16H24A···24H32A···32P48A···48P96A···96AF
order1233446688881212121216···1624···2432···3248···4896···96
size11111111111111111···11···11···11···11···1

96 irreducible representations

dim111111111111
type++
imageC1C2C3C4C6C8C12C16C24C32C48C96
kernelC96C48C32C24C16C12C8C6C4C3C2C1
# reps112224488161632

Matrix representation of C96 in GL2(𝔽17) generated by

814
114
G:=sub<GL(2,GF(17))| [8,11,14,4] >;

C96 in GAP, Magma, Sage, TeX

C_{96}
% in TeX

G:=Group("C96");
// GroupNames label

G:=SmallGroup(96,2);
// by ID

G=gap.SmallGroup(96,2);
# by ID

G:=PCGroup([6,-2,-3,-2,-2,-2,-2,36,50,69,88]);
// Polycyclic

G:=Group<a|a^96=1>;
// generators/relations

Export

Subgroup lattice of C96 in TeX

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