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C₂²×C₃×C₉×C₈₁ #72187606

order	8748
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 25509168
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃²×C₉

Aliases

C₂²×C₃×C₉×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₂₇	C₂²×C₃³
socle, prime radical	C₂²×C₃³	C₃×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

1390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8748 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₉×C₈₁, C₂³×C₃×C₉×C₈₁, C₂²×C₃×C₉×C₂₄₃, …
maximal normal subgroup of	C₂×C₃×C₄×C₉×C₈₁, C₂³×C₃×C₉×C₈₁, C₂²×C₃×C₉×C₂₄₃, …
maximal quotient of	C₂×C₃×C₄×C₉×C₈₁, C₂³×C₃×C₉×C₈₁, C₂²×C₃×C₉×C₂₄₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.