C₈₉×D₂₁₁ #49176502

order	37558
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₉×D₂₁₁
unambiguous semidirect product	C₂₁₁⋊(C₂×C₈₉)

Fitting, socle, Hall	C₈₉×C₂₁₁ ⋊ C₂
derived, Sylow	C₂₁₁ ⋊ C₂×C₈₉

	subgroup	G/H
center, hypercenter	C₈₉	D₂₁₁
commutator, cosocle, hypocenter	C₂₁₁	C₂×C₈₉
Frattini	C₁	G
Fitting, socle	C₈₉×C₂₁₁	C₂
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₈₉

8 conjugacy classes of subgroups.

μ_t(G) = 18779

9523 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37558, 2);