C₉₀₇⋊C₂₇ #37587529

order	24489
automorphism	?
homology	Abelianization (H₁) = C₂₇ · Schur multiplier (H₂) = C₁

Aliases

C₉₀₇⋊C₂₇

C₉₀₇ ⋊ C₂₇

	subgroup	G/H
center, Frattini, hypercenter	C₉	C₉₀₇⋊C₃
commutator, hypocenter	C₉₀₇	C₂₇
Fitting, cosocle	C₉×C₉₀₇	C₃
socle, prime radical	C₃×C₉₀₇	C₉
LCS	G ▷ C₉₀₇
UCS	C₁ ◁ C₉

8 conjugacy classes of subgroups.

μ_t(G) = 24489

Polycyclic presentation:

3^3,907|a^3=b,b^3=c,d^a=d^384

2745 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24489, 6);