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#1043×AGL(1,ℤ/16) #72253191

order	12800
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

#1043×AGL(1,ℤ/16)

Splittings

Fitting	C₅²×AGL(1,ℤ/16) ⋊ C₄
Sylow	C₅² ⋊ C₄×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂	#442×#1043
commutator	C₅²×C₈	C₂²×C₄²
Frattini	C₂×C₈	C₂³×#1043
Fitting	C₅²×AGL(1,ℤ/16)	C₄
socle	C₂×C₅²	C₄×#442
prime radical	C₅⋊D₅×#509	C₂²
cosocle	C₂×C₈×C₅⋊D₅	C₂⁴
hypercenter	AGL(1,ℤ/16)	#1043
hypocenter	C₅²	C₄×AGL(1,ℤ/16)
LCS	G ▷ C₅²×C₈ ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ AGL(1,ℤ/16)

6216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 400

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal quotient of

GAP

Past the SmallGroups library coverage — no SmallGroups id.