C₅×D₃×D₇×C₈₉ #49153181

order	37380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₃×D₇×C₈₉
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₅×C₈₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₅×C₈₉)
unambiguous semidirect product	D₂₁⋊(C₂×C₅×C₈₉)

	subgroup	G/H
center, hypercenter	C₅×C₈₉	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₅×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₈₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₈₉

80 conjugacy classes of subgroups.

μ_t(G) = 9345

6675 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 75);