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G = C91order 91 = 7·13

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C91, also denoted Z91, SmallGroup(91,1)

Series: Derived Chief Lower central Upper central

C1 — C91
C1C13 — C91
C1 — C91
C1 — C91

Generators and relations for C91
 G = < a | a91=1 >


Smallest permutation representation of C91
Regular action on 91 points
Generators in S91
(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)

G:=sub<Sym(91)| (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)>;

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) );

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)])

C91 is a maximal subgroup of   D91  C91⋊C3  C914C3

91 conjugacy classes

class 1 7A···7F13A···13L91A···91BT
order17···713···1391···91
size11···11···11···1

91 irreducible representations

dim1111
type+
imageC1C7C13C91
kernelC91C13C7C1
# reps161272

Matrix representation of C91 in GL1(𝔽547) generated by

100
G:=sub<GL(1,GF(547))| [100] >;

C91 in GAP, Magma, Sage, TeX

C_{91}
% in TeX

G:=Group("C91");
// GroupNames label

G:=SmallGroup(91,1);
// by ID

G=gap.SmallGroup(91,1);
# by ID

G:=PCGroup([2,-7,-13]);
// Polycyclic

G:=Group<a|a^91=1>;
// generators/relations

Export

Subgroup lattice of C91 in TeX

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