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C₂²×C₃³×C₃₂ #72183113

order	3456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 17252352
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂²×C₃³×C₃₂
multiplicative	(ℤ/6111)ˣ, (ℤ/12222)ˣ

Subgroups

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

1680 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃³×C₆₄, C₂×C₃³×C₄×C₃₂, C₂³×C₃³×C₃₂, …
maximal normal subgroup of	C₂²×C₃³×C₆₄, C₂×C₃³×C₄×C₃₂, C₂³×C₃³×C₃₂, …
maximal quotient of	C₂²×C₃³×C₆₄, C₂×C₃³×C₄×C₃₂, C₂³×C₃³×C₃₂, …
automorphism group of	C₇×C₉×C₉₇
outer automorphism group of	C₇×C₉×C₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.