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C₅×C₈×C₁₆×C₂₅ #72193971

order	16000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4096000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅×C₈

Aliases

abelian	C₅×C₈×C₁₆×C₂₅
multiplicative	(ℤ/16441)ˣ, (ℤ/32882)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₅×C₈	C₂²×C₅²
socle, prime radical	C₂²×C₅²	C₄×C₅×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

728 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₈×C₂₅×C₃₂, C₅×C₁₆²×C₂₅, C₂×C₅×C₈×C₁₆×C₂₅
maximal normal subgroup of	C₅×C₈×C₂₅×C₃₂, C₅×C₁₆²×C₂₅, C₂×C₅×C₈×C₁₆×C₂₅
maximal quotient of	C₅×C₈×C₂₅×C₃₂, C₅×C₁₆²×C₂₅, C₂×C₅×C₈×C₁₆×C₂₅
automorphism group of	C₄₁×C₄₀₁
outer automorphism group of	C₄₁×C₄₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.