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G = C94order 94 = 2·47

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C94, also denoted Z94, SmallGroup(94,2)

Series: Derived Chief Lower central Upper central

C1 — C94
C1C47 — C94
C1 — C94
C1 — C94

Generators and relations for C94
 G = < a | a94=1 >


Smallest permutation representation of C94
Regular action on 94 points
Generators in S94
(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)

G:=sub<Sym(94)| (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)>;

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) );

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)])

C94 is a maximal subgroup of   Dic47

94 conjugacy classes

class 1  2 47A···47AT94A···94AT
order1247···4794···94
size111···11···1

94 irreducible representations

dim1111
type++
imageC1C2C47C94
kernelC94C47C2C1
# reps114646

Matrix representation of C94 in GL1(𝔽283) generated by

76
G:=sub<GL(1,GF(283))| [76] >;

C94 in GAP, Magma, Sage, TeX

C_{94}
% in TeX

G:=Group("C94");
// GroupNames label

G:=SmallGroup(94,2);
// by ID

G=gap.SmallGroup(94,2);
# by ID

G:=PCGroup([2,-2,-47]);
// Polycyclic

G:=Group<a|a^94=1>;
// generators/relations

Export

Subgroup lattice of C94 in TeX

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