direct product, cyclic, abelian, monomial
Aliases: C141, also denoted Z141, SmallGroup(141,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C141 |
| C1 — C141 |
| C1 — C141 |
Generators and relations for C141
G = < a | a141=1 >
Smallest permutation representation of C141
►Regular action on 141 points
Generators in S141
(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)
G:=sub<Sym(141)| (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)>;
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) );
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)]])
C141 is a maximal subgroup of
D141
141 conjugacy classes
| class | 1 | 3A | 3B | 47A | ··· | 47AT | 141A | ··· | 141CN |
| order | 1 | 3 | 3 | 47 | ··· | 47 | 141 | ··· | 141 |
| size | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
141 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | |||
| image | C1 | C3 | C47 | C141 |
| kernel | C141 | C47 | C3 | C1 |
| # reps | 1 | 2 | 46 | 92 |
Matrix representation of C141 ►in GL1(𝔽283) generated by
| 257 |
G:=sub<GL(1,GF(283))| [257] >;
C141 in GAP, Magma, Sage, TeX
C_{141} % in TeX
G:=Group("C141"); // GroupNames label
G:=SmallGroup(141,1);
// by ID
G=gap.SmallGroup(141,1);
# by ID
G:=PCGroup([2,-3,-47]);
// Polycyclic
G:=Group<a|a^141=1>;
// generators/relations
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