C₁₇×C₁₉⋊AGL(1,𝔽₁₁) #48001057

order	35530
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₁₉⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	C₁₉⋊(C₁₇×AGL(1,𝔽₁₁))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₁₇×D₁₉)
unambiguous semidirect product	D₂₀₉⋊(C₅×C₁₇)
unambiguous semidirect product	(C₁₇×D₂₀₉)⋊C₅

	subgroup	G/H
center, hypercenter	C₁₇	C₁₉⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇×C₁₉	C₂×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₁₇

32 conjugacy classes of subgroups.

μ_t(G) = 3553

1258 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 22);