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G = C42order 42 = 2·3·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C42, also denoted Z42, SmallGroup(42,6)

Series: Derived Chief Lower central Upper central

C1 — C42
C1C7C21 — C42
C1 — C42
C1 — C42

Generators and relations for C42
 G = < a | a42=1 >


Smallest permutation representation of C42
Regular action on 42 points
Generators in S42
(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)

G:=sub<Sym(42)| (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)>;

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) );

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)])

42 conjugacy classes

class 1  2 3A3B6A6B7A···7F14A···14F21A···21L42A···42L
order1233667···714···1421···2142···42
size1111111···11···11···11···1

42 irreducible representations

dim11111111
type++
imageC1C2C3C6C7C14C21C42
kernelC42C21C14C7C6C3C2C1
# reps1122661212

Matrix representation of C42 in GL1(𝔽43) generated by

18
G:=sub<GL(1,GF(43))| [18] >;

C42 in GAP, Magma, Sage, TeX

C_{42}
% in TeX

G:=Group("C42");
// GroupNames label

G:=SmallGroup(42,6);
// by ID

G=gap.SmallGroup(42,6);
# by ID

G:=PCGroup([3,-2,-3,-7]);
// Polycyclic

G:=Group<a|a^42=1>;
// generators/relations

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