D₂₉×D₃₁⋊C₉ #44569030

order	32364
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₂₉×D₃₁⋊C₉
unambiguous semidirect product	D₃₁⋊(C₉×D₂₉)
unambiguous semidirect product	(D₂₉×D₃₁)⋊C₉
unambiguous semidirect product	(C₂₉×D₃₁⋊C₉)⋊C₂
unambiguous semidirect product	(D₂₉×C₃₁⋊C₉)⋊C₂
unambiguous semidirect product	(C₂₉⋊(D₃₁⋊C₉))⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₂₉×D₃₁⋊C₃
commutator, hypocenter	C₂₉×C₃₁	C₂²×C₉
Fitting, socle, cosocle	C₃×C₂₉×C₃₁	C₂²×C₃
prime radical	C₃×D₂₉×D₃₁	C₃
LCS	G ▷ C₂₉×C₃₁
UCS	C₁ ◁ C₃

60 conjugacy classes of subgroups.

μ_t(G) = 8091

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 16);