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G = C₂₃  order 23

Cyclic group

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

Aliases: C₂₃, also denoted Z₂₃, SmallGroup(23,1)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Generators and relations for C₂₃
 G = < a | a²³=1 >

Character table of C₂₃

(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)

G:=sub<Sym(23)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)>;

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) );

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)]])

G:=TransitiveGroup(23,1);

C₂₃ is a maximal subgroup of   D₂₃  C₂₃⋊C₁₁

Matrix representation of C₂₃ ►in GL₁(𝔽₄₇) generated by

G:=sub<GL(1,GF(47))| [24] >;

C₂₃ in GAP, Magma, Sage, TeX

C_{23}

% in TeX

G:=Group("C23");

// GroupNames label

G:=SmallGroup(23,1);

// by ID

G=gap.SmallGroup(23,1);

# by ID

G:=PCGroup([1,-23]:ExponentLimit:=1);

// Polycyclic

G:=Group<a|a^23=1>;

// generators/relations

Export

Subgroup lattice of C₂₃ in TeX
Character table of C₂₃ in TeX