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G = C31order 31

Cyclic group

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

Aliases: C31, also denoted Z31, SmallGroup(31,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C31
C1 — C31
C1 — C31
C1 — C31
C1 — C31

Generators and relations for C31
 G = < a | a31=1 >


Permutation representations of C31
Regular action on 31 points - transitive group 31T1
Generators in S31
(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)

G:=sub<Sym(31)| (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)>;

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) );

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)])

G:=TransitiveGroup(31,1);

31 conjugacy classes

class 1 31A···31AD
order131···31
size11···1

31 irreducible representations

dim11
type+
imageC1C31
kernelC31C1
# reps130

Matrix representation of C31 in GL1(𝔽311) generated by

113
G:=sub<GL(1,GF(311))| [113] >;

C31 in GAP, Magma, Sage, TeX

C_{31}
% in TeX

G:=Group("C31");
// GroupNames label

G:=SmallGroup(31,1);
// by ID

G=gap.SmallGroup(31,1);
# by ID

G:=PCGroup([1,-31]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^31=1>;
// generators/relations

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