C₃²×C₁₉×AGL(1,𝔽₁₁) #34037864

order	18810
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₁₉×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₃²×C₅×C₁₉)
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₂×C₃²×C₁₉)
unambiguous semidirect product	(C₃×D₁₁)⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	(C₃²×D₁₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₃²×C₁₉×D₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₃²×C₁₉	AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁	C₂×C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₉	C₂×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃²×C₁₉

96 conjugacy classes of subgroups.

μ_t(G) = 1881

1881 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 57);