direct product, cyclic, abelian, monomial
Aliases: C130, also denoted Z130, SmallGroup(130,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C130 |
| C1 — C130 |
| C1 — C130 |
Generators and relations for C130
G = < a | a130=1 >
Smallest permutation representation of C130
►Regular action on 130 points
Generators in S130
(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)
G:=sub<Sym(130)| (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)>;
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) );
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)]])
C130 is a maximal subgroup of
Dic65
130 conjugacy classes
| class | 1 | 2 | 5A | 5B | 5C | 5D | 10A | 10B | 10C | 10D | 13A | ··· | 13L | 26A | ··· | 26L | 65A | ··· | 65AV | 130A | ··· | 130AV |
| order | 1 | 2 | 5 | 5 | 5 | 5 | 10 | 10 | 10 | 10 | 13 | ··· | 13 | 26 | ··· | 26 | 65 | ··· | 65 | 130 | ··· | 130 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
130 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||
| image | C1 | C2 | C5 | C10 | C13 | C26 | C65 | C130 |
| kernel | C130 | C65 | C26 | C13 | C10 | C5 | C2 | C1 |
| # reps | 1 | 1 | 4 | 4 | 12 | 12 | 48 | 48 |
Matrix representation of C130 ►in GL2(𝔽131) generated by
| 71 | 0 |
| 0 | 65 |
G:=sub<GL(2,GF(131))| [71,0,0,65] >;
C130 in GAP, Magma, Sage, TeX
C_{130} % in TeX
G:=Group("C130"); // GroupNames label
G:=SmallGroup(130,4);
// by ID
G=gap.SmallGroup(130,4);
# by ID
G:=PCGroup([3,-2,-5,-13]);
// Polycyclic
G:=Group<a|a^130=1>;
// generators/relations
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