A₄×C₁₉×C₅²⋊C₃ #30685822

order	17100
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	A₄×C₁₉×C₅²⋊C₃
unambiguous semidirect product	(C₂²×C₅²⋊C₃)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₅²×A₄)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂²⋊(C₅²⋊C₃))⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	A₄×C₅²⋊C₃
commutator, cosocle, hypocenter	C₂²×C₅²	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₁₉	C₃²
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₁₉

76 conjugacy classes of subgroups.

μ_t(G) = 1140

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 459);