C₂×C₃×C₁₉×(C₅⋊D₅)⋊C₃ #30685833

order	17100
isoclinism	isoclinic class of (C₅⋊D₅)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₁₉ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₂×C₃×C₁₉×(C₅⋊D₅)⋊C₃
unambiguous semidirect product	(C₂×C₅⋊D₅)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₂×C₃×C₅⋊D₅)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₁₉

160 conjugacy classes of subgroups.

μ_t(G) = 1710

1140 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 470);