C₁₉×D₁₁×AGL(1,𝔽₇) #31798239

order	17556
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×D₁₁×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×C₁₉×D₁₁)
unambiguous semidirect product	(D₇×D₁₁)⋊(C₃×C₁₉)
unambiguous semidirect product	(ΓL(1,𝔽₈)×D₁₁)⋊(C₂×C₁₉)
unambiguous semidirect product	(C₁₁×AGL(1,𝔽₇))⋊(C₂×C₁₉)
unambiguous semidirect product	(C₁₁⋊AGL(1,𝔽₇))⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₁₁×AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₉	C₂²×C₃
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 1463

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 54);