C₁₉×C₉⋊AGL(1,𝔽₁₁) #34037832

order	18810
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₉⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	C₉⋊(C₁₉×AGL(1,𝔽₁₁))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(D₉×C₁₉)
unambiguous semidirect product	D₉₉⋊(C₅×C₁₉)
unambiguous semidirect product	(C₁₉×D₉₉)⋊C₅

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₉×C₁₁	C₂×C₅×C₁₉
Frattini	C₃	C₁₉×C₃⋊AGL(1,𝔽₁₁)
Fitting	C₉×C₁₁×C₁₉	C₂×C₅
socle	C₃×C₁₁×C₁₉	C₅×D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₁₉

48 conjugacy classes of subgroups.

μ_t(G) = 1881

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 25);