Finite Group Databasebeta

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C₃×C₄×C₉×C₈₉ #72188339

order	9612
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 19008
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₄×C₉×C₈₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃²×C₈₉
socle, prime radical	C₂×C₃²×C₈₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9612 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈×C₉×C₈₉, C₂×C₃×C₄×C₉×C₈₉, C₃×C₄×C₂₇×C₈₉, …
maximal normal subgroup of	C₃×C₈×C₉×C₈₉, C₂×C₃×C₄×C₉×C₈₉, C₃×C₄×C₂₇×C₈₉, …
maximal quotient of	C₃×C₈×C₉×C₈₉, C₂×C₃×C₄×C₉×C₈₉, C₃×C₄×C₂₇×C₈₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.