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AGL(1,ℤ/8)×ΓL(1,𝔽₁₆) #14416674

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

AGL(1,ℤ/8)×ΓL(1,𝔽₁₆)

Splittings

Fitting	C₃×C₅×AGL(1,ℤ/8) ⋊ C₄
Hall	C₃×C₅ ⋊ C₄×AGL(1,ℤ/8)
Sylow	C₅ ⋊ Dic₃×AGL(1,ℤ/8)
Sylow	C₃ ⋊ AGL(1,𝔽₅)×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂	C₂×D₄×ΓL(1,𝔽₁₆)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂³×ΓL(1,𝔽₁₆)
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×D₅×AGL(1,ℤ/8)	C₂
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	AGL(1,ℤ/8)	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₅)×AGL(1,ℤ/8), #72229732, ΓL(1,𝔽₁₆)×#453, …
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×AGL(1,ℤ/8), #72229732, ΓL(1,𝔽₁₆)×#453
maximal quotient of	#72230457, #72259593

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142372);