Finite Group Databasebeta

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C₃²×C₄²×C₉² #72190118

order	11664
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 117546246144
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁵×C₄×C₉

Aliases

C₃²×C₄²×C₉²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃²	C₂²×C₃⁴
socle, prime radical	C₂²×C₃⁴	C₂²×C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

15990 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11664 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₈×C₉², C₂×C₃²×C₄²×C₉²
maximal normal subgroup of	C₃²×C₄×C₈×C₉², C₂×C₃²×C₄²×C₉²
maximal quotient of	C₃²×C₄×C₈×C₉², C₂×C₃²×C₄²×C₉²

GAP

Past the SmallGroups library coverage — no SmallGroups id.