Copied to
clipboard

G = C41order 41

Cyclic group

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

Aliases: C41, also denoted Z41, SmallGroup(41,1)

Series: Derived Chief Lower central Upper central Jennings

C1 — C41
C1 — C41
C1 — C41
C1 — C41
C1 — C41

Generators and relations for C41
 G = < a | a41=1 >


Smallest permutation representation of C41
Regular action on 41 points
Generators in S41
(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)

G:=sub<Sym(41)| (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)>;

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) );

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)])

41 conjugacy classes

class 1 41A···41AN
order141···41
size11···1

41 irreducible representations

dim11
type+
imageC1C41
kernelC41C1
# reps140

Matrix representation of C41 in GL1(𝔽83) generated by

68
G:=sub<GL(1,GF(83))| [68] >;

C41 in GAP, Magma, Sage, TeX

C_{41}
% in TeX

G:=Group("C41");
// GroupNames label

G:=SmallGroup(41,1);
// by ID

G=gap.SmallGroup(41,1);
# by ID

G:=PCGroup([1,-41]:ExponentLimit:=1);
// Polycyclic

G:=Group<a|a^41=1>;
// generators/relations

׿
×
𝔽