D₉×C₂₁₁₁ #49184386

order	37998
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₁₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₂₁₁₁
unambiguous semidirect product	C₉⋊(C₂×C₂₁₁₁)

Fitting, Hall	C₉×C₂₁₁₁ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₂₁₁₁

	subgroup	G/H
center, hypercenter	C₂₁₁₁	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₂₁₁₁
Frattini	C₃	D₃×C₂₁₁₁
Fitting	C₉×C₂₁₁₁	C₂
socle	C₃×C₂₁₁₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂₁₁₁

12 conjugacy classes of subgroups.

μ_t(G) = 18999

12666 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37998, 2);