C₅×C₁₉×C₃⋊(D₁₉⋊C₃) #44570597

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×C₃⋊(D₁₉⋊C₃)
unambiguous semidirect product	C₃⋊(C₅×C₁₉×D₁₉⋊C₃)
unambiguous semidirect product	(C₁₉⋊C₃)⋊(C₅×D₃×C₁₉)
unambiguous semidirect product	D₅₇⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	(C₅×D₅₇)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₃⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₅×C₁₉

84 conjugacy classes of subgroups.

μ_t(G) = 1710

1710 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 181);