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C₃³×C₄²×C₁₆ #72185997

order	6912
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2208301056
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄³

Aliases

C₃³×C₄²×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

7812 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃³×C₄²×C₃₂, C₃³×C₄×C₈×C₁₆, C₂×C₃³×C₄²×C₁₆, …
maximal normal subgroup of	C₃³×C₄²×C₃₂, C₃³×C₄×C₈×C₁₆, C₂×C₃³×C₄²×C₁₆, …
maximal quotient of	C₃³×C₄²×C₃₂, C₃³×C₄×C₈×C₁₆, C₂×C₃³×C₄²×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.