#28353240

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃	#17987310
commutator, prime radical, cosocle	C₃⁴×C₁₉	C₃²
Frattini	C₃⁴	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6866	C₃
socle	C₃×C₁₉	#6856
hypercenter	#6866	C₁₉⋊C₃
hypocenter	C₁₉	#10624476
LCS	G ▷ C₃⁴×C₁₉ ▷ C₃³×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6866

154 conjugacy classes of subgroups.

μ_t(G) = 513

Polycyclic presentation:

3^6,19|a^3=f,b^3=f,b^a=bc,c^a=cd,e^a=ef,g^a=g^7,c^b=ce,d^b=df,g^b=g^11

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 604);