#46798461

order	33777
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₁₃₉ ⋊ #6861

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₃₉⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₃₉	C₃²
Frattini	C₃³	C₃×C₁₃₉⋊C₃
Fitting	C₃²⋊C₉×C₁₃₉	C₃
socle	C₃²×C₁₃₉	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6861
LCS	G ▷ C₃³×C₁₃₉ ▷ C₃²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

50 conjugacy classes of subgroups.

μ_t(G) = 11259

Polycyclic presentation:

3^5,139|a^3=e,b^3=d,b^a=bc,c^a=cd,f^a=f^96,c^b=ce

1553 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33777, 85);