direct product, cyclic, abelian, monomial
Aliases: C58, also denoted Z58, SmallGroup(58,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C58 |
| C1 — C58 |
| C1 — C58 |
Generators and relations for C58
G = < a | a58=1 >
Smallest permutation representation of C58
►Regular action on 58 points
Generators in S58
(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 47 48 49 50 51 52 53 54 55 56 57 58)
G:=sub<Sym(58)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)]])
C58 is a maximal subgroup of
Dic29
58 conjugacy classes
| class | 1 | 2 | 29A | ··· | 29AB | 58A | ··· | 58AB |
| order | 1 | 2 | 29 | ··· | 29 | 58 | ··· | 58 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C29 | C58 |
| kernel | C58 | C29 | C2 | C1 |
| # reps | 1 | 1 | 28 | 28 |
Matrix representation of C58 ►in GL1(𝔽59) generated by
| 11 |
G:=sub<GL(1,GF(59))| [11] >;
C58 in GAP, Magma, Sage, TeX
C_{58} % in TeX
G:=Group("C58"); // GroupNames label
G:=SmallGroup(58,2);
// by ID
G=gap.SmallGroup(58,2);
# by ID
G:=PCGroup([2,-2,-29]);
// Polycyclic
G:=Group<a|a^58=1>;
// generators/relations
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