#38733328

order	24867
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₃₀₇ ⋊ #733

	subgroup	G/H
center	C₃	C₃²⋊(C₃₀₇⋊C₃)
commutator, prime radical, cosocle	C₃²×C₃₀₇	C₃²
Frattini	C₃²	C₃×C₃₀₇⋊C₃
Fitting	3₋¹⁺²×C₃₀₇	C₃
socle	C₃×C₃₀₇	H(3,𝔽₃)
hypercenter	3₋¹⁺²	C₃₀₇⋊C₃
hypocenter	C₃₀₇	#733
LCS	G ▷ C₃²×C₃₀₇ ▷ C₃×C₃₀₇ ▷ C₃₀₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ 3₋¹⁺²

26 conjugacy classes of subgroups.

μ_t(G) = 8289

Polycyclic presentation:

3^4,307|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^b=e^289

1139 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24867, 36);