C₂×C₅²×D₉×C₁₉ #30685623

order	17100
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅²×D₉×C₁₉
unambiguous semidirect product	C₉⋊(C₂²×C₅²×C₁₉)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₅²×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₉	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₅²×C₁₉
Frattini	C₃	C₂×C₅²×D₃×C₁₉
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle	C₂×C₃×C₅²×C₁₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₅²×C₁₉

240 conjugacy classes of subgroups.

μ_t(G) = 8550

5700 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 260);