C₁₉×C₄₂₁⋊C₃ #37562078

order	23997
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₄₂₁⋊C₃
unambiguous semidirect product	C₄₂₁⋊(C₃×C₁₉)

Fitting, socle, Hall	C₁₉×C₄₂₁ ⋊ C₃
derived, Sylow	C₄₂₁ ⋊ C₃×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	C₄₂₁⋊C₃
commutator, cosocle, hypocenter	C₄₂₁	C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₄₂₁	C₃
LCS	G ▷ C₄₂₁
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

μ_t(G) = 7999

2717 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23997, 2);