C₂×C₅×D₃×C₇×C₈₉ #49153227

order	37380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₃×C₇×C₈₉
unambiguous semidirect product	C₃⋊(C₂²×C₅×C₇×C₈₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅×C₇×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₈₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₇×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₈₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₇×C₈₉

80 conjugacy classes of subgroups.

μ_t(G) = 18690

18690 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 121);