C₅×D₃×C₇×D₈₉ #49153178

order	37380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₃×C₇×D₈₉
unambiguous semidirect product	(D₃×C₈₉)⋊(C₂×C₅×C₇)
unambiguous semidirect product	(C₃×D₈₉)⋊(C₂×C₅×C₇)
unambiguous semidirect product	D₂₆₇⋊(C₂×C₅×C₇)

	subgroup	G/H
center, hypercenter	C₅×C₇	D₃×D₈₉
commutator, cosocle, hypocenter	C₃×C₈₉	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₈₉	C₂²
LCS	G ▷ C₃×C₈₉
UCS	C₁ ◁ C₅×C₇

80 conjugacy classes of subgroups.

μ_t(G) = 9345

4830 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 72);