direct product, cyclic, abelian, monomial
Aliases: C134, also denoted Z134, SmallGroup(134,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C134 |
| C1 — C134 |
| C1 — C134 |
Generators and relations for C134
G = < a | a134=1 >
Smallest permutation representation of C134
►Regular action on 134 points
Generators in S134
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134)
G:=sub<Sym(134)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134)]])
C134 is a maximal subgroup of
Dic67
134 conjugacy classes
| class | 1 | 2 | 67A | ··· | 67BN | 134A | ··· | 134BN |
| order | 1 | 2 | 67 | ··· | 67 | 134 | ··· | 134 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
134 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C67 | C134 |
| kernel | C134 | C67 | C2 | C1 |
| # reps | 1 | 1 | 66 | 66 |
Matrix representation of C134 ►in GL1(𝔽269) generated by
| 253 |
G:=sub<GL(1,GF(269))| [253] >;
C134 in GAP, Magma, Sage, TeX
C_{134} % in TeX
G:=Group("C134"); // GroupNames label
G:=SmallGroup(134,2);
// by ID
G=gap.SmallGroup(134,2);
# by ID
G:=PCGroup([2,-2,-67]);
// Polycyclic
G:=Group<a|a^134=1>;
// generators/relations
Export