C₁₉×C₆₆₁⋊C₃ #49179271

order	37677
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₆₆₁⋊C₃
unambiguous semidirect product	C₆₆₁⋊(C₃×C₁₉)

Fitting, socle, Hall	C₁₉×C₆₆₁ ⋊ C₃
derived, Sylow	C₆₆₁ ⋊ C₃×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	C₆₆₁⋊C₃
commutator, cosocle, hypocenter	C₆₆₁	C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₆₆₁	C₃
LCS	G ▷ C₆₆₁
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

μ_t(G) = 12559

4237 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37677, 2);