C₁₉⋊C₃×C₃₄₉ #34091086

order	19893
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₄₉ · Schur multiplier (H₂) = C₁

Aliases

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

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

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

8 conjugacy classes of subgroups.

μ_t(G) = 6631

3141 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19893, 1);