direct product, cyclic, abelian, monomial
Aliases: C44, also denoted Z44, SmallGroup(44,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — 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)]])
C44 is a maximal subgroup of
C11⋊C8 Dic22 D44
44 conjugacy classes
| class | 1 | 2 | 4A | 4B | 11A | ··· | 11J | 22A | ··· | 22J | 44A | ··· | 44T |
| order | 1 | 2 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||
| image | C1 | C2 | C4 | C11 | C22 | C44 |
| kernel | C44 | C22 | C11 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 10 | 10 | 20 |
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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