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G = C69order 69 = 3·23

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C69, also denoted Z69, SmallGroup(69,1)

Series: Derived Chief Lower central Upper central

C1 — C69
C1C23 — C69
C1 — C69
C1 — C69

Generators and relations for C69
 G = < a | a69=1 >


Smallest permutation representation of C69
Regular action on 69 points
Generators in S69
(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)

G:=sub<Sym(69)| (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)>;

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) );

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)])

C69 is a maximal subgroup of   D69

69 conjugacy classes

class 1 3A3B23A···23V69A···69AR
order13323···2369···69
size1111···11···1

69 irreducible representations

dim1111
type+
imageC1C3C23C69
kernelC69C23C3C1
# reps122244

Matrix representation of C69 in GL1(𝔽139) generated by

37
G:=sub<GL(1,GF(139))| [37] >;

C69 in GAP, Magma, Sage, TeX

C_{69}
% in TeX

G:=Group("C69");
// GroupNames label

G:=SmallGroup(69,1);
// by ID

G=gap.SmallGroup(69,1);
# by ID

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

G:=Group<a|a^69=1>;
// generators/relations

Export

Subgroup lattice of C69 in TeX

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