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G = C47order 47

Cyclic group

p-group, cyclic, elementary abelian, simple, monomial

Aliases: C47, also denoted Z47, SmallGroup(47,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C47
C1 — C47
C1 — C47
C1 — C47
C1 — C47

Generators and relations for C47
 G = < a | a47=1 >


Smallest permutation representation of C47
Regular action on 47 points
Generators in S47
(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)

G:=sub<Sym(47)| (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)>;

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) );

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)])

47 conjugacy classes

class 1 47A···47AT
order147···47
size11···1

47 irreducible representations

dim11
type+
imageC1C47
kernelC47C1
# reps146

Matrix representation of C47 in GL1(𝔽283) generated by

230
G:=sub<GL(1,GF(283))| [230] >;

C47 in GAP, Magma, Sage, TeX

C_{47}
% in TeX

G:=Group("C47");
// GroupNames label

G:=SmallGroup(47,1);
// by ID

G=gap.SmallGroup(47,1);
# by ID

G:=PCGroup([1,-47]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^47=1>;
// generators/relations

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