C₂×C₃×C₅×C₁₉×C₁₉⋊C₃ #44570618

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₅×C₁₉×C₁₉⋊C₃
unambiguous semidirect product	(C₂×C₁₉)⋊(C₃²×C₅×C₁₉)
unambiguous semidirect product	(C₂×C₃×C₁₉)⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	(C₂×C₅×C₁₉)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₂×C₃×C₅×C₁₉)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₉²	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₅×C₁₉

144 conjugacy classes of subgroups.

μ_t(G) = 1710

5130 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 202);