(C₃³⋊C₁₃)⋊C₂₇ #23748635

order	9477
automorphism	?
homology	Abelianization (H₁) = C₂₇ · Schur multiplier (H₂) = C₁

Aliases

(C₃³⋊C₁₃)⋊C₂₇

C₃³⋊C₁₃ ⋊ C₂₇

	subgroup	G/H
center, Frattini, hypercenter	C₉	(C₃³⋊C₁₃)⋊C₃
commutator, hypocenter	C₃³⋊C₁₃	C₂₇
Fitting	C₃³×C₉	C₁₃⋊C₃
socle	C₃⁴	C₁₃⋊C₉
prime radical	C₃×C₃³⋊C₁₃	C₉
cosocle	C₉×C₃³⋊C₁₃	C₃
LCS	G ▷ C₃³⋊C₁₃
UCS	C₁ ◁ C₉

46 conjugacy classes of subgroups.

Polycyclic presentation:

3,13,3^5|a^3=f,f^3=g,b^a=b^3,c^a=cde,d^a=de^2,c^b=cd,d^b=de,e^b=c^2e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4044);