C₂×C₅×D₃×C₁₉ #11765909

order	1140
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₃×C₁₉
unambiguous semidirect product	C₃⋊(C₂²×C₅×C₁₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 570

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1140, 37);