C₃×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃))) #13091722

order	1458
isoclinism	isoclinic class of C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₃¹⁰

Aliases

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

Fitting, socle, Sylow	C₃⁶ ⋊ C₂
derived	C₃⁵ ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))
commutator, cosocle, hypocenter	C₃⁵	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃⁶	C₂
LCS	G ▷ C₃⁵
UCS	C₁ ◁ C₃

36308 conjugacy classes of subgroups.

μ_t(G) = 486

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1796);