p-group, cyclic, elementary abelian, simple, monomial
Aliases: C131, also denoted Z131, SmallGroup(131,1)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
| C1 — C131 |
| C1 — C131 |
| C1 — C131 |
| C1 — C131 |
Generators and relations for C131
G = < a | a131=1 >
Smallest permutation representation of C131
►Regular action on 131 points
Generators in S131
(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 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131)
G:=sub<Sym(131)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131)]])
C131 is a maximal subgroup of
D131
131 conjugacy classes
| class | 1 | 131A | ··· | 131DZ |
| order | 1 | 131 | ··· | 131 |
| size | 1 | 1 | ··· | 1 |
131 irreducible representations
| dim | 1 | 1 |
| type | + | |
| image | C1 | C131 |
| kernel | C131 | C1 |
| # reps | 1 | 130 |
Matrix representation of C131 ►in GL1(𝔽263) generated by
| 83 |
G:=sub<GL(1,GF(263))| [83] >;
C131 in GAP, Magma, Sage, TeX
C_{131} % in TeX
G:=Group("C131"); // GroupNames label
G:=SmallGroup(131,1);
// by ID
G=gap.SmallGroup(131,1);
# by ID
G:=PCGroup([1,-131]:ExponentLimit:=1);
// Polycyclic
G:=Group<a|a^131=1>;
// generators/relations
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