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G = C38order 38 = 2·19

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C38, also denoted Z38, SmallGroup(38,2)

Series: Derived Chief Lower central Upper central

C1 — C38
C1C19 — C38
C1 — C38
C1 — C38

Generators and relations for C38
 G = < a | a38=1 >


Smallest permutation representation of C38
Regular action on 38 points
Generators in S38
(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)

G:=sub<Sym(38)| (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)>;

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) );

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)])

38 conjugacy classes

class 1  2 19A···19R38A···38R
order1219···1938···38
size111···11···1

38 irreducible representations

dim1111
type++
imageC1C2C19C38
kernelC38C19C2C1
# reps111818

Matrix representation of C38 in GL1(𝔽191) generated by

122
G:=sub<GL(1,GF(191))| [122] >;

C38 in GAP, Magma, Sage, TeX

C_{38}
% in TeX

G:=Group("C38");
// GroupNames label

G:=SmallGroup(38,2);
// by ID

G=gap.SmallGroup(38,2);
# by ID

G:=PCGroup([2,-2,-19]);
// Polycyclic

G:=Group<a|a^38=1>;
// generators/relations

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