C₂×C₃⋊D₃×C₂₉×C₃₁ #44569140

order	32364
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉×C₃₁ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊D₃×C₂₉×C₃₁
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₂₉×C₃₁)

	subgroup	G/H
center, hypercenter	C₂×C₂₉×C₃₁	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₂₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₂₉×C₃₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₂₉×C₃₁

120 conjugacy classes of subgroups.

μ_t(G) = 16182

10788 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 126);