Copied to
clipboard

G = C36order 36 = 22·32

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C36, also denoted Z36, SmallGroup(36,2)

Series: Derived Chief Lower central Upper central

C1 — C36
C1C3C6C18 — C36
C1 — C36
C1 — C36

Generators and relations for C36
 G = < a | a36=1 >


Smallest permutation representation of C36
Regular action on 36 points
Generators in S36
(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)

G:=sub<Sym(36)| (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)>;

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) );

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)])

Polynomial with Galois group C36 over ℚ
actionf(x)Disc(f)
36T1x36+x35+x34+x33+x32+x31+x30+x29+x28+x27+x26+x25+x24+x23+x22+x21+x20+x19+x18+x17+x16+x15+x14+x13+x12+x11+x10+x9+x8+x7+x6+x5+x4+x3+x2+x+13735

36 conjugacy classes

class 1  2 3A3B4A4B6A6B9A···9F12A12B12C12D18A···18F36A···36L
order123344669···91212121218···1836···36
size111111111···111111···11···1

36 irreducible representations

dim111111111
type++
imageC1C2C3C4C6C9C12C18C36
kernelC36C18C12C9C6C4C3C2C1
# reps1122264612

Matrix representation of C36 in GL1(𝔽37) generated by

17
G:=sub<GL(1,GF(37))| [17] >;

C36 in GAP, Magma, Sage, TeX

C_{36}
% in TeX

G:=Group("C36");
// GroupNames label

G:=SmallGroup(36,2);
// by ID

G=gap.SmallGroup(36,2);
# by ID

G:=PCGroup([4,-2,-3,-2,-3,24,53]);
// Polycyclic

G:=Group<a|a^36=1>;
// generators/relations

׿
×
𝔽