C₅×D₉×C₃₈₉ #46855845

order	35010
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₃₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₉×C₃₈₉
unambiguous semidirect product	C₉⋊(C₂×C₅×C₃₈₉)

	subgroup	G/H
center, hypercenter	C₅×C₃₈₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₃₈₉
Frattini	C₃	C₅×D₃×C₃₈₉
Fitting	C₅×C₉×C₃₈₉	C₂
socle	C₃×C₅×C₃₈₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₃₈₉

24 conjugacy classes of subgroups.

μ_t(G) = 17505

11670 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35010, 5);