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G = C₂₅  order 25 = 5²

Cyclic group

p-group, cyclic, abelian, monomial

Aliases: C₂₅, also denoted Z₂₅, SmallGroup(25,1)

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

Generators and relations for C₂₅
 G = < a | a²⁵=1 >

Character table of C₂₅

(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)

G:=sub<Sym(25)| (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)>;

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) );

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)]])

G:=TransitiveGroup(25,1);

C₂₅ is a maximal subgroup of   D₂₅  C₁₂₅  5_-¹⁺²  C₁₁⋊C₂₅  C₂⁴⋊C₂₅
C₂₅ is a maximal quotient of   C₁₂₅  C₁₁⋊C₂₅  C₂⁴⋊C₂₅

Matrix representation of C₂₅ ►in GL₁(𝔽₁₀₁) generated by

G:=sub<GL(1,GF(101))| [80] >;

C₂₅ in GAP, Magma, Sage, TeX

C_{25}

% in TeX

G:=Group("C25");

// GroupNames label

G:=SmallGroup(25,1);

// by ID

G=gap.SmallGroup(25,1);

# by ID

G:=PCGroup([2,-5,-5,10]:ExponentLimit:=1);

// Polycyclic

G:=Group<a|a^25=1>;

// generators/relations

Export

Subgroup lattice of C₂₅ in TeX
Character table of C₂₅ in TeX