direct product, cyclic, abelian, monomial
Aliases: C140, also denoted Z140, SmallGroup(140,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C140 |
| C1 — C140 |
| C1 — C140 |
Generators and relations for C140
G = < a | a140=1 >
Smallest permutation representation of C140
►Regular action on 140 points
Generators in S140
(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)
G:=sub<Sym(140)| (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)>;
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) );
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)]])
C140 is a maximal subgroup of
C35⋊3C8 Dic70 D140
140 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 5C | 5D | 7A | ··· | 7F | 10A | 10B | 10C | 10D | 14A | ··· | 14F | 20A | ··· | 20H | 28A | ··· | 28L | 35A | ··· | 35X | 70A | ··· | 70X | 140A | ··· | 140AV |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 7 | ··· | 7 | 10 | 10 | 10 | 10 | 14 | ··· | 14 | 20 | ··· | 20 | 28 | ··· | 28 | 35 | ··· | 35 | 70 | ··· | 70 | 140 | ··· | 140 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
140 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||||||
| image | C1 | C2 | C4 | C5 | C7 | C10 | C14 | C20 | C28 | C35 | C70 | C140 |
| kernel | C140 | C70 | C35 | C28 | C20 | C14 | C10 | C7 | C5 | C4 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 6 | 4 | 6 | 8 | 12 | 24 | 24 | 48 |
Matrix representation of C140 ►in GL1(𝔽281) generated by
| 114 |
G:=sub<GL(1,GF(281))| [114] >;
C140 in GAP, Magma, Sage, TeX
C_{140} % in TeX
G:=Group("C140"); // GroupNames label
G:=SmallGroup(140,4);
// by ID
G=gap.SmallGroup(140,4);
# by ID
G:=PCGroup([4,-2,-5,-7,-2,280]);
// Polycyclic
G:=Group<a|a^140=1>;
// generators/relations
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