C₆₁×C₁₆₉⋊C₃ #44525730

order	30927
automorphism	?
homology	Abelianization (H₁) = C₃×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₁×C₁₆₉⋊C₃
unambiguous semidirect product	C₁₆₉⋊(C₃×C₆₁)

Fitting, Hall	C₆₁×C₁₆₉ ⋊ C₃
derived, Sylow	C₁₆₉ ⋊ C₃×C₆₁

	subgroup	G/H
center, hypercenter	C₆₁	C₁₆₉⋊C₃
commutator, cosocle, hypocenter	C₁₆₉	C₃×C₆₁
Frattini	C₁₃	C₁₃⋊C₃×C₆₁
Fitting	C₆₁×C₁₆₉	C₃
socle	C₁₃×C₆₁	C₁₃⋊C₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₆₁

12 conjugacy classes of subgroups.

μ_t(G) = 10309

3599 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30927, 2);