C₅×C₁₇×D₁₁₇ #34091027

order	19890
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇×D₁₁₇
unambiguous semidirect product	C₉⋊(C₅×C₁₇×D₁₃)
unambiguous semidirect product	C₁₃⋊(C₅×C₁₇×D₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂×C₅×C₁₇
Frattini	C₃	C₅×C₁₇×D₃₉
Fitting	C₅×C₉×C₁₃×C₁₇	C₂
socle	C₃×C₅×C₁₃×C₁₇	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₅×C₁₇

48 conjugacy classes of subgroups.

μ_t(G) = 9945

5100 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 12);