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C₅×C₃₂×C₁₀₁ #72194127

order	16160
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₈×C₂₅ (order 6400) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₈×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₁₆₀
abelian	C₅×C₃₂×C₁₀₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₅×C₁₀₁
socle, prime radical	C₂×C₅×C₁₀₁	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16160 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₁₆₀, D₃₂₃₂₀
Fitting subgroup of	Dic₈₀₈₀, D₁₆₁₆₀
maximal subgroup of	C₅×C₆₄×C₁₀₁, C₂×C₅×C₃₂×C₁₀₁, Dic₈₀₈₀, …
maximal normal subgroup of	C₅×C₆₄×C₁₀₁, C₂×C₅×C₃₂×C₁₀₁, Dic₈₀₈₀, …
maximal quotient of	C₅×C₆₄×C₁₀₁, C₂×C₅×C₃₂×C₁₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.