D₅×C₁₉×D₃₁⋊C₃ #47977654

order	35340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×C₁₉×D₃₁⋊C₃
unambiguous semidirect product	D₃₁⋊(C₃×D₅×C₁₉)
unambiguous semidirect product	(D₅×D₃₁)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₅×D₃₁⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(D₅×C₃₁⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(C₅⋊(D₃₁⋊C₃))⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₃₁⋊C₃
commutator, cosocle, hypocenter	C₅×C₃₁	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₃₁	C₂²×C₃
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 2945

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 126);