#28353726

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃²

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₁₉⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₉	C₃³
Frattini	C₃³	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624588
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

202 conjugacy classes of subgroups.

μ_t(G) = 4617

Polycyclic presentation:

3^6,19|a^3=f,b^3=f,c^3=e,b^a=bd,d^a=de,d^b=df,g^b=g^7

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 1090);