Finite Group Databasebeta

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C₃²×C₄×C₅²×C₉ #72186987

order	8100
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 22394880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₅

Aliases

C₃²×C₄×C₅²×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃³×C₅²
socle, prime radical	C₂×C₃³×C₅²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

1200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₅²×C₈×C₉, C₂×C₃²×C₄×C₅²×C₉, C₃²×C₄×C₅²×C₂₇, …
maximal normal subgroup of	C₃²×C₅²×C₈×C₉, C₂×C₃²×C₄×C₅²×C₉, C₃²×C₄×C₅²×C₂₇, …
maximal quotient of	C₃²×C₅²×C₈×C₉, C₂×C₃²×C₄×C₅²×C₉, C₃²×C₄×C₅²×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.