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C₂³×C₃²×C₈₁ #72185085

order	5832
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 35271936
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂³×C₃²×C₈₁
multiplicative	(ℤ/10269)ˣ, (ℤ/20538)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

1504 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₄×C₈₁, C₂⁴×C₃²×C₈₁, C₂³×C₃²×C₂₄₃, …
maximal normal subgroup of	C₂²×C₃²×C₄×C₈₁, C₂⁴×C₃²×C₈₁, C₂³×C₃²×C₂₄₃, …
maximal quotient of	C₂²×C₃²×C₄×C₈₁, C₂⁴×C₃²×C₈₁, C₂³×C₃²×C₂₄₃, …
automorphism group of	C₇×C₉×C₁₆₃
outer automorphism group of	C₇×C₉×C₁₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.