#14670854

order	2816
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Splittings

Sylow

C₁₁ ⋊ #13015

Subgroups

	subgroup	G/H
center	C₂³	C₂×#4323
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1969	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1969	D₁₁
hypocenter	C₁₁	#13015
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1969

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2816

Polycyclic presentation:

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

Conjugacy classes & character table

278 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 86649);