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G = C40order 40 = 23·5

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C40, also denoted Z40, SmallGroup(40,2)

Series: Derived Chief Lower central Upper central

C1 — C40
C1C2C4C20 — C40
C1 — C40
C1 — C40

Generators and relations for C40
 G = < a | a40=1 >


Smallest permutation representation of C40
Regular action on 40 points
Generators in S40
(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)

G:=sub<Sym(40)| (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)>;

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) );

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)])

40 conjugacy classes

class 1  2 4A4B5A5B5C5D8A8B8C8D10A10B10C10D20A···20H40A···40P
order1244555588881010101020···2040···40
size11111111111111111···11···1

40 irreducible representations

dim11111111
type++
imageC1C2C4C5C8C10C20C40
kernelC40C20C10C8C5C4C2C1
# reps112444816

Matrix representation of C40 in GL1(𝔽41) generated by

34
G:=sub<GL(1,GF(41))| [34] >;

C40 in GAP, Magma, Sage, TeX

C_{40}
% in TeX

G:=Group("C40");
// GroupNames label

G:=SmallGroup(40,2);
// by ID

G=gap.SmallGroup(40,2);
# by ID

G:=PCGroup([4,-2,-5,-2,-2,40,34]);
// Polycyclic

G:=Group<a|a^40=1>;
// generators/relations

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