C₁₇×C₃⋊D₃×C₁₀₉ #45688690

order	33354
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₁₀₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₇×C₃⋊D₃×C₁₀₉
unambiguous semidirect product	C₃⋊(D₃×C₁₇×C₁₀₉)

	subgroup	G/H
center, hypercenter	C₁₇×C₁₀₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₇×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₁₀₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₇×C₁₀₉

48 conjugacy classes of subgroups.

μ_t(G) = 16677

11118 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33354, 33);