C₅×D₉×C₃₅₉ #44568182

order	32310
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₃₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₉×C₃₅₉
unambiguous semidirect product	C₉⋊(C₂×C₅×C₃₅₉)

	subgroup	G/H
center, hypercenter	C₅×C₃₅₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₃₅₉
Frattini	C₃	C₅×D₃×C₃₅₉
Fitting	C₅×C₉×C₃₅₉	C₂
socle	C₃×C₅×C₃₅₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₃₅₉

24 conjugacy classes of subgroups.

μ_t(G) = 16155

10770 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32310, 5);