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C₄²×C₅²×C₁₃ #72184575

order	5200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 552960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄×C₅

Aliases

C₄²×C₅²×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₅²×C₁₃
socle, prime radical	C₂²×C₅²×C₁₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅²×C₈×C₁₃, C₂×C₄²×C₅²×C₁₃, C₃×C₄²×C₅²×C₁₃, …
maximal normal subgroup of	C₄×C₅²×C₈×C₁₃, C₂×C₄²×C₅²×C₁₃, C₃×C₄²×C₅²×C₁₃, …
maximal quotient of	C₄×C₅²×C₈×C₁₃, C₂×C₄²×C₅²×C₁₃, C₃×C₄²×C₅²×C₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.