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#14644273

order	2816
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Splittings

C₁₁ ⋊ #8149

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator, socle	C₂³×C₁₁	C₂×C₄²
Fitting	C₄×C₁₁×C₂²⋊C₈	C₂
prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄×C₂²⋊C₈	D₁₁
hypocenter	C₁₁	#8149
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₂²⋊C₈

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1408

Polycyclic presentation:

2^8,11|a^2=e,b^2=f,c^2=e,e^2=g,f^2=h,b^a=bd,c^a=ch,i^a=i^10,c^b=cg,i^b=i^10,i^c=i^10

Conjugacy classes & character table

488 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 60068);