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C₃³×C₄²×C₃₂ #72192011

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4416602112
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄³

Aliases

C₃³×C₄²×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₆	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₂²×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

9912 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃³×C₄²×C₆₄, C₃³×C₄×C₈×C₃₂, C₂×C₃³×C₄²×C₃₂
maximal normal subgroup of	C₃³×C₄²×C₆₄, C₃³×C₄×C₈×C₃₂, C₂×C₃³×C₄²×C₃₂
maximal quotient of	C₃³×C₄²×C₆₄, C₃³×C₄×C₈×C₃₂, C₂×C₃³×C₄²×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.