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G = C2×C22order 44 = 22·11

Abelian group of type [2,22]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C22, SmallGroup(44,4)

Series: Derived Chief Lower central Upper central

C1 — C2×C22
C1C11C22 — C2×C22
C1 — C2×C22
C1 — C2×C22

Generators and relations for C2×C22
 G = < a,b | a2=b22=1, ab=ba >


Smallest permutation representation of C2×C22
Regular action on 44 points
Generators in S44
(1 41)(2 42)(3 43)(4 44)(5 23)(6 24)(7 25)(8 26)(9 27)(10 28)(11 29)(12 30)(13 31)(14 32)(15 33)(16 34)(17 35)(18 36)(19 37)(20 38)(21 39)(22 40)
(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)| (1,41)(2,42)(3,43)(4,44)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40), (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( (1,41)(2,42)(3,43)(4,44)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40), (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([(1,41),(2,42),(3,43),(4,44),(5,23),(6,24),(7,25),(8,26),(9,27),(10,28),(11,29),(12,30),(13,31),(14,32),(15,33),(16,34),(17,35),(18,36),(19,37),(20,38),(21,39),(22,40)], [(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 2A2B2C11A···11J22A···22AD
order122211···1122···22
size11111···11···1

44 irreducible representations

dim1111
type++
imageC1C2C11C22
kernelC2×C22C22C22C2
# reps131030

Matrix representation of C2×C22 in GL2(𝔽23) generated by

220
01
,
100
07
G:=sub<GL(2,GF(23))| [22,0,0,1],[10,0,0,7] >;

C2×C22 in GAP, Magma, Sage, TeX

C_2\times C_{22}
% in TeX

G:=Group("C2xC22");
// GroupNames label

G:=SmallGroup(44,4);
// by ID

G=gap.SmallGroup(44,4);
# by ID

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

G:=Group<a,b|a^2=b^22=1,a*b=b*a>;
// generators/relations

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