#14656737

order	2816
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#10622836
commutator, prime radical, cosocle	C₂⁵×C₁₁	C₂³
Frattini	C₂⁵	C₂²×D₁₁
Fitting	C₁₁×#2483	C₂
socle	C₂²×C₁₁	#392
hypercenter	#2483	D₁₁
hypocenter	C₁₁	#10339
LCS	G ▷ C₂⁵×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #2483

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

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

μ_t(G) = 352

Polycyclic presentation:

2^8,11|a^2=g,b^2=g,c^2=h,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,e^b=eh,d^c=dg,i^c=i^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 72532);