D₅×C₁₉×D₁₉⋊C₃ #36343202

order	21660
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×C₁₉×D₁₉⋊C₃
unambiguous semidirect product	D₁₉⋊(C₃×D₅×C₁₉)
unambiguous semidirect product	(D₅×D₁₉)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₅×D₁₉⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(D₅×C₁₉⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(C₅⋊(D₁₉⋊C₃))⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂²×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₁₉

92 conjugacy classes of subgroups.

μ_t(G) = 570

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 126);