direct product, cyclic, abelian, monomial
Aliases: C93, also denoted Z93, SmallGroup(93,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C93 |
| C1 — C93 |
| C1 — C93 |
Generators and relations for C93
G = < a | a93=1 >
Smallest permutation representation of C93
►Regular action on 93 points
Generators in S93
(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 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93)
G:=sub<Sym(93)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93)]])
C93 is a maximal subgroup of
D93 C31⋊C9
93 conjugacy classes
| class | 1 | 3A | 3B | 31A | ··· | 31AD | 93A | ··· | 93BH |
| order | 1 | 3 | 3 | 31 | ··· | 31 | 93 | ··· | 93 |
| size | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
93 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C31 | C93 |
| kernel | C93 | C31 | C3 | C1 |
| # reps | 1 | 2 | 30 | 60 |
Matrix representation of C93 ►in GL1(𝔽373) generated by
| 9 |
G:=sub<GL(1,GF(373))| [9] >;
C93 in GAP, Magma, Sage, TeX
C_{93} % in TeX
G:=Group("C93"); // GroupNames label
G:=SmallGroup(93,2);
// by ID
G=gap.SmallGroup(93,2);
# by ID
G:=PCGroup([2,-3,-31]);
// Polycyclic
G:=Group<a|a^93=1>;
// generators/relations
Export