D₃×C₁₉⋊C₃×C₁₀₉ #49152182

order	37278
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₀₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉⋊C₃×C₁₀₉
unambiguous semidirect product	C₃⋊(C₂×C₁₉⋊C₃×C₁₀₉)
unambiguous semidirect product	(D₃×C₁₉)⋊(C₃×C₁₀₉)

	subgroup	G/H
center, hypercenter	C₁₀₉	D₃×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₀₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₁₀₉

36 conjugacy classes of subgroups.

μ_t(G) = 6213

2943 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37278, 98);