direct product, cyclic, abelian, monomial
Aliases: C62, also denoted Z62, SmallGroup(62,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C62 |
| C1 — C62 |
| C1 — C62 |
Generators and relations for C62
G = < a | a62=1 >
Smallest permutation representation of C62
►Regular action on 62 points
Generators in S62
(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 59 60 61 62)
G:=sub<Sym(62)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62)]])
C62 is a maximal subgroup of
Dic31
62 conjugacy classes
| class | 1 | 2 | 31A | ··· | 31AD | 62A | ··· | 62AD |
| order | 1 | 2 | 31 | ··· | 31 | 62 | ··· | 62 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
62 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C31 | C62 |
| kernel | C62 | C31 | C2 | C1 |
| # reps | 1 | 1 | 30 | 30 |
Matrix representation of C62 ►in GL1(𝔽311) generated by
| 298 |
G:=sub<GL(1,GF(311))| [298] >;
C62 in GAP, Magma, Sage, TeX
C_{62} % in TeX
G:=Group("C62"); // GroupNames label
G:=SmallGroup(62,2);
// by ID
G=gap.SmallGroup(62,2);
# by ID
G:=PCGroup([2,-2,-31]);
// Polycyclic
G:=Group<a|a^62=1>;
// generators/relations
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