C₂×C₃×C₇×D₅×C₈₉ #49153223

order	37380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₇×D₅×C₈₉
unambiguous semidirect product	C₅⋊(C₂²×C₃×C₇×C₈₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃×C₇×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₈₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₇×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₈₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₇×C₈₉

80 conjugacy classes of subgroups.

μ_t(G) = 18690

14952 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 117);