Finite Group Databasebeta

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C₃²×C₄×C₉×C₃₂ #72188984

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11943936
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄

Aliases

C₃²×C₄×C₉×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₁₆	C₂²×C₃³
socle, prime radical	C₂²×C₃³	C₂×C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

1800 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₉×C₆₄, C₃²×C₈×C₉×C₃₂, C₂×C₃²×C₄×C₉×C₃₂, …
maximal normal subgroup of	C₃²×C₄×C₉×C₆₄, C₃²×C₈×C₉×C₃₂, C₂×C₃²×C₄×C₉×C₃₂, …
maximal quotient of	C₃²×C₄×C₉×C₆₄, C₃²×C₈×C₉×C₃₂, C₂×C₃²×C₄×C₉×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.