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G = C43order 43

Cyclic group

p-group, cyclic, elementary abelian, simple, monomial

Aliases: C43, also denoted Z43, SmallGroup(43,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C43
C1 — C43
C1 — C43
C1 — C43
C1 — C43

Generators and relations for C43
 G = < a | a43=1 >


Smallest permutation representation of C43
Regular action on 43 points
Generators in S43
(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)

G:=sub<Sym(43)| (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)>;

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) );

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)])

43 conjugacy classes

class 1 43A···43AP
order143···43
size11···1

43 irreducible representations

dim11
type+
imageC1C43
kernelC43C1
# reps142

Matrix representation of C43 in GL1(𝔽173) generated by

124
G:=sub<GL(1,GF(173))| [124] >;

C43 in GAP, Magma, Sage, TeX

C_{43}
% in TeX

G:=Group("C43");
// GroupNames label

G:=SmallGroup(43,1);
// by ID

G=gap.SmallGroup(43,1);
# by ID

G:=PCGroup([1,-43]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^43=1>;
// generators/relations

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