direct product, cyclic, abelian, monomial
Aliases: C63, also denoted Z63, SmallGroup(63,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C63 |
| C1 — C63 |
| C1 — C63 |
Generators and relations for C63
G = < a | a63=1 >
Smallest permutation representation of C63
►Regular action on 63 points
Generators in S63
(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 63)
G:=sub<Sym(63)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)]])
C63 is a maximal subgroup of
D63 C7⋊C27 C63⋊C3 C63⋊3C3
63 conjugacy classes
| class | 1 | 3A | 3B | 7A | ··· | 7F | 9A | ··· | 9F | 21A | ··· | 21L | 63A | ··· | 63AJ |
| order | 1 | 3 | 3 | 7 | ··· | 7 | 9 | ··· | 9 | 21 | ··· | 21 | 63 | ··· | 63 |
| size | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
63 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | |||||
| image | C1 | C3 | C7 | C9 | C21 | C63 |
| kernel | C63 | C21 | C9 | C7 | C3 | C1 |
| # reps | 1 | 2 | 6 | 6 | 12 | 36 |
Matrix representation of C63 ►in GL1(𝔽127) generated by
| 115 |
G:=sub<GL(1,GF(127))| [115] >;
C63 in GAP, Magma, Sage, TeX
C_{63} % in TeX
G:=Group("C63"); // GroupNames label
G:=SmallGroup(63,2);
// by ID
G=gap.SmallGroup(63,2);
# by ID
G:=PCGroup([3,-3,-7,-3,63]);
// Polycyclic
G:=Group<a|a^63=1>;
// generators/relations
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