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#737×C₁₀₁ #22551145

order	8181
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₀₁ · Schur multiplier (H₂) = C₃²

Aliases

#737×C₁₀₁

Subgroups

	subgroup	G/H
center	C₉×C₁₀₁	C₃²
commutator, Frattini	C₃	C₃³×C₁₀₁
socle	C₃×C₁₀₁	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₀₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3333 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#6872, C₁₀₁×#6873, C₁₀₁×#6903, …
maximal normal subgroup of	C₁₀₁×#6872, C₁₀₁×#6873, C₁₀₁×#6903, …
maximal quotient of	C₁₀₁×#6887, C₉×H(3,𝔽₃)×C₁₀₁, C₉×3₋¹⁺²×C₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8181, 14);