Finite Group Databasebeta

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C₂×C₃×C₄²×C₁₁² #72190056

order	11616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 40550400
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄×C₁₁

Aliases

C₂×C₃×C₄²×C₁₁²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₃×C₁₁²
socle, prime radical	C₂³×C₃×C₁₁²	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

1512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₈×C₁₁², C₃×C₄³×C₁₁², C₂²×C₃×C₄²×C₁₁²
maximal normal subgroup of	C₂×C₃×C₄×C₈×C₁₁², C₃×C₄³×C₁₁², C₂²×C₃×C₄²×C₁₁²
maximal quotient of	C₂×C₃×C₄×C₈×C₁₁², C₃×C₄³×C₁₁², C₂²×C₃×C₄²×C₁₁²

GAP

Past the SmallGroups library coverage — no SmallGroups id.