#14670517

order	2816
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Sylow

C₁₁ ⋊ #12957

Subgroups

	subgroup	G/H
center	C₂²	#10622398
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#362	C₂
socle	C₂²×C₁₁	#442
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#362	D₁₁
hypocenter	C₁₁	#12957
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#362

396 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 704

Polycyclic presentation:

2^8,11|a^2=f,b^2=fg,c^2=h,d^2=g,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,d^b=dg,e^b=egh,f^b=fh,g^b=gh,i^b=i^10,d^c=dgh,e^c=eg,f^c=fh,g^c=gh

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 86312);