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#14643138

order	2816
automorphism	?
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₂×C₄²

Aliases

No aliases for this group.

Splittings

C₁₁ ⋊ #7843

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₄²×C₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄²×C₈	D₁₁
hypocenter	C₁₁	#7843
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×C₈

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2816

Polycyclic presentation:

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

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 58933);