C₃×A₄×C₁₉×C₂₃ #30628647

order	15732
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉×C₂₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×A₄×C₁₉×C₂₃
unambiguous semidirect product	C₂²⋊(C₃²×C₁₉×C₂₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₃×C₁₉×C₂₃)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₂²×C₃×C₂₃)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₉×C₂₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₁₉×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₉×C₂₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₉×C₂₃

56 conjugacy classes of subgroups.

μ_t(G) = 5244

5244 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 109);