C₁₃⋊C₉×D₈₅ #34091037

order	19890
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₉×D₈₅
unambiguous semidirect product	C₅⋊(D₁₇×C₁₃⋊C₉)
unambiguous semidirect product	C₁₇⋊(D₅×C₁₃⋊C₉)
unambiguous semidirect product	(C₁₃×D₈₅)⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₃⋊C₃×D₈₅
commutator, hypocenter	C₅×C₁₃×C₁₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₁₃×D₈₅	C₃
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₃

48 conjugacy classes of subgroups.

μ_t(G) = 9945

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 22);