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G = C119order 119 = 7·17

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C119, also denoted Z119, SmallGroup(119,1)

Series: Derived Chief Lower central Upper central

C1 — C119
C1C17 — C119
C1 — C119
C1 — C119

Generators and relations for C119
 G = < a | a119=1 >


Smallest permutation representation of C119
Regular action on 119 points
Generators in S119
(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)

G:=sub<Sym(119)| (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)>;

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) );

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)])

C119 is a maximal subgroup of   D119

119 conjugacy classes

class 1 7A···7F17A···17P119A···119CR
order17···717···17119···119
size11···11···11···1

119 irreducible representations

dim1111
type+
imageC1C7C17C119
kernelC119C17C7C1
# reps161696

Matrix representation of C119 in GL2(𝔽239) generated by

710
098
G:=sub<GL(2,GF(239))| [71,0,0,98] >;

C119 in GAP, Magma, Sage, TeX

C_{119}
% in TeX

G:=Group("C119");
// GroupNames label

G:=SmallGroup(119,1);
// by ID

G=gap.SmallGroup(119,1);
# by ID

G:=PCGroup([2,-7,-17]);
// Polycyclic

G:=Group<a|a^119=1>;
// generators/relations

Export

Subgroup lattice of C119 in TeX

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