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G = C140order 140 = 22·5·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C140, also denoted Z140, SmallGroup(140,4)

Series: Derived Chief Lower central Upper central

C1 — C140
C1C2C14C70 — 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   C353C8  Dic70  D140

140 conjugacy classes

class 1  2 4A4B5A5B5C5D7A···7F10A10B10C10D14A···14F20A···20H28A···28L35A···35X70A···70X140A···140AV
order124455557···71010101014···1420···2028···2835···3570···70140···140
size111111111···111111···11···11···11···11···11···1

140 irreducible representations

dim111111111111
type++
imageC1C2C4C5C7C10C14C20C28C35C70C140
kernelC140C70C35C28C20C14C10C7C5C4C2C1
# reps1124646812242448

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

Export

Subgroup lattice of C140 in TeX

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