C₃₁⋊C₂₅₆ #21519864

order	7936
automorphism	?
homology	Abelianization (H₁) = C₂₅₆ · Schur multiplier (H₂) = C₁

Aliases

C₃₁⋊C₂₅₆

C₃₁ ⋊ C₂₅₆

	subgroup	G/H
center, Frattini, hypercenter	C₁₂₈	D₃₁
commutator, hypocenter	C₃₁	C₂₅₆
Fitting	C₃₁×C₁₂₈	C₂
socle	C₂×C₃₁	C₁₂₈
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₂₈

18 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,31|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^30

2176 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7936, 56093);