Go

G = C₃₃  order 33 = 3·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C₃₃, also denoted Z₃₃, SmallGroup(33,1)

Series: Derived ►Chief ►Lower central ►Upper central

Generators and relations for C₃₃
 G = < a | a³³=1 >

(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)

G:=sub<Sym(33)| (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)>;

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) );

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)]])

C₃₃ is a maximal subgroup of   D₃₃

33 conjugacy classes

33 irreducible representations

Matrix representation of C₃₃ ►in GL₁(𝔽₆₇) generated by

G:=sub<GL(1,GF(67))| [65] >;

C₃₃ in GAP, Magma, Sage, TeX

C_{33}

% in TeX

G:=Group("C33");

// GroupNames label

G:=SmallGroup(33,1);

// by ID

G=gap.SmallGroup(33,1);

# by ID

G:=PCGroup([2,-3,-11]);

// Polycyclic

G:=Group<a|a^33=1>;

// generators/relations

Export

Subgroup lattice of C₃₃ in TeX