C₉₉₁⋊C₃₂ #44540356

order	31712
automorphism	?
homology	Abelianization (H₁) = C₃₂ · Schur multiplier (H₂) = C₁

Aliases

C₉₉₁⋊C₃₂

C₉₉₁ ⋊ C₃₂

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₉₉₁
commutator, hypocenter	C₉₉₁	C₃₂
Fitting, cosocle	C₁₆×C₉₉₁	C₂
socle, prime radical	C₂×C₉₉₁	C₁₆
LCS	G ▷ C₉₉₁
UCS	C₁ ◁ C₁₆

12 conjugacy classes of subgroups.

μ_t(G) = 31712

Polycyclic presentation:

2^5,991|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^990

7952 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31712, 52);