C₁₉×C₃⋊(C₅⋊(D₁₉⋊C₃)) #44570608

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

Aliases

direct product	C₁₉×C₃⋊(C₅⋊(D₁₉⋊C₃))
unambiguous semidirect product	C₃⋊(C₁₉×C₅⋊(D₁₉⋊C₃))
unambiguous semidirect product	C₅⋊(C₁₉×C₃⋊(D₁₉⋊C₃))
unambiguous semidirect product	(C₁₉⋊C₃)⋊(C₁₉×D₁₅)
unambiguous semidirect product	D₂₈₅⋊(C₃×C₁₉)

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

84 conjugacy classes of subgroups.

μ_t(G) = 1710

1368 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 192);