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G = C44order 44 = 22·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C44, also denoted Z44, SmallGroup(44,2)

Series: Derived Chief Lower central Upper central

C1 — C44
C1C2C22 — C44
C1 — C44
C1 — C44

Generators and relations for C44
 G = < a | a44=1 >


Smallest permutation representation of C44
Regular action on 44 points
Generators in S44
(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)

G:=sub<Sym(44)| (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)>;

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) );

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)])

44 conjugacy classes

class 1  2 4A4B11A···11J22A···22J44A···44T
order124411···1122···2244···44
size11111···11···11···1

44 irreducible representations

dim111111
type++
imageC1C2C4C11C22C44
kernelC44C22C11C4C2C1
# reps112101020

Matrix representation of C44 in GL1(𝔽89) generated by

47
G:=sub<GL(1,GF(89))| [47] >;

C44 in GAP, Magma, Sage, TeX

C_{44}
% in TeX

G:=Group("C44");
// GroupNames label

G:=SmallGroup(44,2);
// by ID

G=gap.SmallGroup(44,2);
# by ID

G:=PCGroup([3,-2,-11,-2,66]);
// Polycyclic

G:=Group<a|a^44=1>;
// generators/relations

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