C₃×C₂₉×C₁₂₇⋊C₃ #45684113

order	33147
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₂₉×C₁₂₇⋊C₃
unambiguous semidirect product	C₁₂₇⋊(C₃²×C₂₉)
unambiguous semidirect product	(C₃×C₁₂₇)⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×C₁₂₇)⋊C₃²
unambiguous semidirect product	(C₃×C₂₉×C₁₂₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₂₉	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₂₉

24 conjugacy classes of subgroups.

μ_t(G) = 11049

3915 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33147, 5);