C₃×D₃×C₁₉×D₂₃ #30628620

order	15732
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₃×C₁₉×D₂₃
unambiguous semidirect product	(D₃×C₂₃)⋊(C₂×C₃×C₁₉)
unambiguous semidirect product	(C₃×D₂₃)⋊(C₂×C₃×C₁₉)
unambiguous semidirect product	D₆₉⋊(C₂×C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₃×D₂₃
commutator, cosocle, hypocenter	C₃×C₂₃	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉×C₂₃	C₂²
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₃×C₁₉

88 conjugacy classes of subgroups.

μ_t(G) = 2622

2223 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 82);