Finite Group Databasebeta

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C₃×C₄×C₉×C₈₁ #72187591

order	8748
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8503056
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃²×C₉

Aliases

C₃×C₄×C₉×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₂₇	C₂×C₃³
socle, prime radical	C₂×C₃³	C₂×C₃×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

834 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8748 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈×C₉×C₈₁, C₂×C₃×C₄×C₉×C₈₁, C₃×C₄×C₉×C₂₄₃, …
maximal normal subgroup of	C₃×C₈×C₉×C₈₁, C₂×C₃×C₄×C₉×C₈₁, C₃×C₄×C₉×C₂₄₃, …
maximal quotient of	C₃×C₈×C₉×C₈₁, C₂×C₃×C₄×C₉×C₈₁, C₃×C₄×C₉×C₂₄₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.