C₂×C₃²×D₅×C₈₉ #30630906

order	16020
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₈₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃²×D₅×C₈₉
unambiguous semidirect product	C₅⋊(C₂²×C₃²×C₈₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃²×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₈₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃²×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₈₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²×C₈₉

120 conjugacy classes of subgroups.

μ_t(G) = 8010

6408 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 111);