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G = C74order 74 = 2·37

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C74, also denoted Z74, SmallGroup(74,2)

Series: Derived Chief Lower central Upper central

C1 — C74
C1C37 — C74
C1 — C74
C1 — C74

Generators and relations for C74
 G = < a | a74=1 >


Smallest permutation representation of C74
Regular action on 74 points
Generators in S74
(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)

G:=sub<Sym(74)| (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)>;

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) );

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)])

C74 is a maximal subgroup of   Dic37

74 conjugacy classes

class 1  2 37A···37AJ74A···74AJ
order1237···3774···74
size111···11···1

74 irreducible representations

dim1111
type++
imageC1C2C37C74
kernelC74C37C2C1
# reps113636

Matrix representation of C74 in GL1(𝔽149) generated by

69
G:=sub<GL(1,GF(149))| [69] >;

C74 in GAP, Magma, Sage, TeX

C_{74}
% in TeX

G:=Group("C74");
// GroupNames label

G:=SmallGroup(74,2);
// by ID

G=gap.SmallGroup(74,2);
# by ID

G:=PCGroup([2,-2,-37]);
// Polycyclic

G:=Group<a|a^74=1>;
// generators/relations

Export

Subgroup lattice of C74 in TeX

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