Finite Group Databasebeta

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C₂²×C₃²×C₄×C₉² #72190129

order	11664
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 235092492288
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃⁵×C₉

Aliases

C₂²×C₃²×C₄×C₉²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃²	C₂³×C₃⁴
socle, prime radical	C₂³×C₃⁴	C₂×C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

28782 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	C₂²×C₃²×C₈×C₉², C₂×C₃²×C₄²×C₉², C₂³×C₃²×C₄×C₉²
maximal normal subgroup of	C₂²×C₃²×C₈×C₉², C₂×C₃²×C₄²×C₉², C₂³×C₃²×C₄×C₉²
maximal quotient of	C₂²×C₃²×C₈×C₉², C₂×C₃²×C₄²×C₉², C₂³×C₃²×C₄×C₉²

GAP

Past the SmallGroups library coverage — no SmallGroups id.