C₁₁₂₃⋊C₂₇ #44476407

order	30321
automorphism	?
homology	Abelianization (H₁) = C₂₇ · Schur multiplier (H₂) = C₁

Aliases

C₁₁₂₃⋊C₂₇

C₁₁₂₃ ⋊ C₂₇

	subgroup	G/H
center, Frattini, hypercenter	C₉	C₁₁₂₃⋊C₃
commutator, hypocenter	C₁₁₂₃	C₂₇
Fitting, cosocle	C₉×C₁₁₂₃	C₃
socle, prime radical	C₃×C₁₁₂₃	C₉
LCS	G ▷ C₁₁₂₃
UCS	C₁ ◁ C₉

8 conjugacy classes of subgroups.

μ_t(G) = 30321

Polycyclic presentation:

3^3,1123|a^3=b,b^3=c,d^a=d^33

3393 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30321, 6);