C₁₉×C₄₀₉⋊C₃ #37552152

order	23313
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₄₀₉⋊C₃
unambiguous semidirect product	C₄₀₉⋊(C₃×C₁₉)

Fitting, socle, Hall	C₁₉×C₄₀₉ ⋊ C₃
derived, Sylow	C₄₀₉ ⋊ C₃×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	C₄₀₉⋊C₃
commutator, cosocle, hypocenter	C₄₀₉	C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₄₀₉	C₃
LCS	G ▷ C₄₀₉
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

μ_t(G) = 7771

2641 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23313, 2);