#16846878

order	3968
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₃₁ ⋊ #2030

	subgroup	G/H
center	C₂²	#11758514
commutator, prime radical, cosocle	C₂⁴×C₃₁	C₂³
Frattini	C₂⁴	C₂²×D₃₁
Fitting	C₃₁×#381	C₂
socle	C₂²×C₃₁	#120
hypercenter	#381	D₃₁
hypocenter	C₃₁	#2030
LCS	G ▷ C₂⁴×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #381

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 992

Polycyclic presentation:

2^7,31|a^2=d,b^2=d,c^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^30

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 5677);