C₂×C₅×D₁₉×C₈₉ #46799059

order	33820
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₉×C₈₉
unambiguous semidirect product	C₁₉⋊(C₂²×C₅×C₈₉)
unambiguous semidirect product	(C₂×C₁₉)⋊(C₂×C₅×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₈₉	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₅×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₈₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅×C₈₉

40 conjugacy classes of subgroups.

μ_t(G) = 16910

9790 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33820, 30);