#49144388

order	36693
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

C₁₅₁ ⋊ #6858

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₅₁⋊C₃)
commutator, prime radical, cosocle	C₃³×C₁₅₁	C₃²
Frattini	C₃³	C₃×C₁₅₁⋊C₃
Fitting	C₃²⋊C₉×C₁₅₁	C₃
socle	C₃²×C₁₅₁	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₁₅₁⋊C₃
hypocenter	C₁₅₁	#6858
LCS	G ▷ C₃³×C₁₅₁ ▷ C₃²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

60 conjugacy classes of subgroups.

μ_t(G) = 12231

Polycyclic presentation:

3^5,151|a^3=d,b^3=d,b^a=bc,c^a=cd,f^a=f^32,c^b=ce

1685 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36693, 76);