C₂×D₅×ΓL(1,𝔽₈)×C₈₉ #49153156

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

Aliases

direct product	C₂×D₅×ΓL(1,𝔽₈)×C₈₉
unambiguous semidirect product	C₅⋊(C₂²×ΓL(1,𝔽₈)×C₈₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×ΓL(1,𝔽₈)×C₈₉)
unambiguous semidirect product	(C₂×C₇×D₅)⋊(C₃×C₈₉)
unambiguous semidirect product	(C₂×C₇×D₅×C₈₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₈₉	D₅×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₈₉	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₈₉

80 conjugacy classes of subgroups.

μ_t(G) = 6230

3560 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 50);