C₁₉×C₃₄₉⋊C₃ #34091087

order	19893
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₃₄₉⋊C₃
unambiguous semidirect product	C₃₄₉⋊(C₃×C₁₉)

Fitting, socle, Hall	C₁₉×C₃₄₉ ⋊ C₃
derived, Sylow	C₃₄₉ ⋊ C₃×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	C₃₄₉⋊C₃
commutator, cosocle, hypocenter	C₃₄₉	C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₃₄₉	C₃
LCS	G ▷ C₃₄₉
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

μ_t(G) = 6631

2261 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19893, 2);