direct product, cyclic, abelian, monomial
Aliases: C46, also denoted Z46, SmallGroup(46,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C46 |
| C1 — C46 |
| C1 — C46 |
Generators and relations for C46
G = < a | a46=1 >
Smallest permutation representation of C46
►Regular action on 46 points
Generators in S46
(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 45 46)
G:=sub<Sym(46)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)]])
C46 is a maximal subgroup of
Dic23
46 conjugacy classes
| class | 1 | 2 | 23A | ··· | 23V | 46A | ··· | 46V |
| order | 1 | 2 | 23 | ··· | 23 | 46 | ··· | 46 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
46 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C23 | C46 |
| kernel | C46 | C23 | C2 | C1 |
| # reps | 1 | 1 | 22 | 22 |
Matrix representation of C46 ►in GL1(𝔽47) generated by
| 19 |
G:=sub<GL(1,GF(47))| [19] >;
C46 in GAP, Magma, Sage, TeX
C_{46} % in TeX
G:=Group("C46"); // GroupNames label
G:=SmallGroup(46,2);
// by ID
G=gap.SmallGroup(46,2);
# by ID
G:=PCGroup([2,-2,-23]);
// Polycyclic
G:=Group<a|a^46=1>;
// generators/relations
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