D₇×D₁₅×C₈₉ #49153197

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

Aliases

direct product	D₇×D₁₅×C₈₉
unambiguous semidirect product	(C₃×D₇)⋊(D₅×C₈₉)
unambiguous semidirect product	(C₅×D₇)⋊(D₃×C₈₉)

	subgroup	G/H
center, hypercenter	C₈₉	D₇×D₁₅
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₈₉	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₈₉

80 conjugacy classes of subgroups.

μ_t(G) = 9345

4005 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 91);