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G = C92order 92 = 22·23

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C92, also denoted Z92, SmallGroup(92,2)

Series: Derived Chief Lower central Upper central

C1 — C92
C1C2C46 — C92
C1 — C92
C1 — C92

Generators and relations for C92
 G = < a | a92=1 >


Smallest permutation representation of C92
Regular action on 92 points
Generators in S92
(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)

G:=sub<Sym(92)| (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)>;

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) );

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)])

C92 is a maximal subgroup of   C23⋊C8  Dic46  D92

92 conjugacy classes

class 1  2 4A4B23A···23V46A···46V92A···92AR
order124423···2346···4692···92
size11111···11···11···1

92 irreducible representations

dim111111
type++
imageC1C2C4C23C46C92
kernelC92C46C23C4C2C1
# reps112222244

Matrix representation of C92 in GL1(𝔽277) generated by

269
G:=sub<GL(1,GF(277))| [269] >;

C92 in GAP, Magma, Sage, TeX

C_{92}
% in TeX

G:=Group("C92");
// GroupNames label

G:=SmallGroup(92,2);
// by ID

G=gap.SmallGroup(92,2);
# by ID

G:=PCGroup([3,-2,-23,-2,138]);
// Polycyclic

G:=Group<a|a^92=1>;
// generators/relations

Export

Subgroup lattice of C92 in TeX

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