direct product, cyclic, abelian, monomial
Aliases: C142, also denoted Z142, SmallGroup(142,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C142 |
| C1 — C142 |
| C1 — C142 |
Generators and relations for C142
G = < a | a142=1 >
Smallest permutation representation of C142
►Regular action on 142 points
Generators in S142
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142)
G:=sub<Sym(142)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142)]])
C142 is a maximal subgroup of
Dic71
142 conjugacy classes
| class | 1 | 2 | 71A | ··· | 71BR | 142A | ··· | 142BR |
| order | 1 | 2 | 71 | ··· | 71 | 142 | ··· | 142 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
142 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C71 | C142 |
| kernel | C142 | C71 | C2 | C1 |
| # reps | 1 | 1 | 70 | 70 |
Matrix representation of C142 ►in GL1(𝔽569) generated by
| 350 |
G:=sub<GL(1,GF(569))| [350] >;
C142 in GAP, Magma, Sage, TeX
C_{142} % in TeX
G:=Group("C142"); // GroupNames label
G:=SmallGroup(142,2);
// by ID
G=gap.SmallGroup(142,2);
# by ID
G:=PCGroup([2,-2,-71]);
// Polycyclic
G:=Group<a|a^142=1>;
// generators/relations
Export