C₄₃⋊C₇₂₉ #44531882

order	31347
automorphism	?
homology	Abelianization (H₁) = C₇₂₉ · Schur multiplier (H₂) = C₁

Aliases

C₄₃⋊C₇₂₉

C₄₃ ⋊ C₇₂₉

	subgroup	G/H
center, Frattini, hypercenter	C₂₄₃	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₇₂₉
Fitting, cosocle	C₄₃×C₂₄₃	C₃
socle, prime radical	C₃×C₄₃	C₂₄₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂₄₃

14 conjugacy classes of subgroups.

μ_t(G) = 31347

Polycyclic presentation:

3^6,43|a^3=b,b^3=c,c^3=d,d^3=e,e^3=f,g^a=g^36

4131 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 505);