direct product, cyclic, abelian, monomial
Aliases: C92, also denoted Z92, SmallGroup(92,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C92 |
| C1 — C92 |
| C1 — C92 |
Generators and relations for C92
G = < a | a92=1 >
Smallest permutation representation of C92
►Regular action on 92 points
Generators in S92
(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)
G:=sub<Sym(92)| (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)>;
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) );
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)]])
C92 is a maximal subgroup of
C23⋊C8 Dic46 D92
92 conjugacy classes
| class | 1 | 2 | 4A | 4B | 23A | ··· | 23V | 46A | ··· | 46V | 92A | ··· | 92AR |
| order | 1 | 2 | 4 | 4 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
92 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||
| image | C1 | C2 | C4 | C23 | C46 | C92 |
| kernel | C92 | C46 | C23 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 22 | 22 | 44 |
Matrix representation of C92 ►in GL1(𝔽277) generated by
| 269 |
G:=sub<GL(1,GF(277))| [269] >;
C92 in GAP, Magma, Sage, TeX
C_{92} % in TeX
G:=Group("C92"); // GroupNames label
G:=SmallGroup(92,2);
// by ID
G=gap.SmallGroup(92,2);
# by ID
G:=PCGroup([3,-2,-23,-2,138]);
// Polycyclic
G:=Group<a|a^92=1>;
// generators/relations
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