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G = C39order 39 = 3·13

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C39, also denoted Z39, SmallGroup(39,2)

Series: Derived Chief Lower central Upper central

C1 — C39
C1C13 — C39
C1 — C39
C1 — C39

Generators and relations for C39
 G = < a | a39=1 >


Smallest permutation representation of C39
Regular action on 39 points
Generators in S39
(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)

G:=sub<Sym(39)| (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)>;

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) );

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)])

39 conjugacy classes

class 1 3A3B13A···13L39A···39X
order13313···1339···39
size1111···11···1

39 irreducible representations

dim1111
type+
imageC1C3C13C39
kernelC39C13C3C1
# reps121224

Matrix representation of C39 in GL1(𝔽79) generated by

25
G:=sub<GL(1,GF(79))| [25] >;

C39 in GAP, Magma, Sage, TeX

C_{39}
% in TeX

G:=Group("C39");
// GroupNames label

G:=SmallGroup(39,2);
// by ID

G=gap.SmallGroup(39,2);
# by ID

G:=PCGroup([2,-3,-13]);
// Polycyclic

G:=Group<a|a^39=1>;
// generators/relations

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