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C₂×C₅²×C₈×C₂₃ #72187938

order	9200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 168960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂×C₅²×C₈×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₅²×C₂₃
socle, prime radical	C₂²×C₅²×C₂₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅²×C₁₆×C₂₃, C₄×C₅²×C₈×C₂₃, C₂²×C₅²×C₈×C₂₃, …
maximal normal subgroup of	C₂×C₅²×C₁₆×C₂₃, C₄×C₅²×C₈×C₂₃, C₂²×C₅²×C₈×C₂₃, …
maximal quotient of	C₂×C₅²×C₁₆×C₂₃, C₄×C₅²×C₈×C₂₃, C₂²×C₅²×C₈×C₂₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.