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G = C37order 37

Cyclic group

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

Aliases: C37, also denoted Z37, SmallGroup(37,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C37
C1 — C37
C1 — C37
C1 — C37
C1 — C37

Generators and relations for C37
 G = < a | a37=1 >


Smallest permutation representation of C37
Regular action on 37 points
Generators in S37
(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)

G:=sub<Sym(37)| (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)>;

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) );

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)])

37 conjugacy classes

class 1 37A···37AJ
order137···37
size11···1

37 irreducible representations

dim11
type+
imageC1C37
kernelC37C1
# reps136

Matrix representation of C37 in GL1(𝔽149) generated by

85
G:=sub<GL(1,GF(149))| [85] >;

C37 in GAP, Magma, Sage, TeX

C_{37}
% in TeX

G:=Group("C37");
// GroupNames label

G:=SmallGroup(37,1);
// by ID

G=gap.SmallGroup(37,1);
# by ID

G:=PCGroup([1,-37]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^37=1>;
// generators/relations

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