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AGL(1,ℤ/8)×PSU(3,𝔽₂)⋊C₃ #72220175

order	6912
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²×C₃

Aliases

AGL(1,ℤ/8)×PSU(3,𝔽₂)⋊C₃

Splittings

C₃²×AGL(1,ℤ/8) ⋊ SL(2,𝔽₃)

Subgroups

	subgroup	G/H
center	C₂	C₂×D₄×PSU(3,𝔽₂)⋊C₃
commutator, cosocle	C₄×PSU(3,𝔽₂)	C₂³×C₃
Frattini	C₄	C₂³×PSU(3,𝔽₂)⋊C₃
Fitting	C₃²×AGL(1,ℤ/8)	SL(2,𝔽₃)
socle	C₂×C₃²	C₂×D₄×SL(2,𝔽₃)
hypercenter	AGL(1,ℤ/8)	PSU(3,𝔽₂)⋊C₃
hypocenter	PSU(3,𝔽₂)	C₃×AGL(1,ℤ/8)
LCS	G ▷ C₄×PSU(3,𝔽₂) ▷ C₂×PSU(3,𝔽₂) ▷ PSU(3,𝔽₂)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

1646 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,ℤ/8)×AGL(2,𝔽₃)
maximal normal subgroup of	AGL(1,ℤ/8)×AGL(2,𝔽₃)

GAP

Past the SmallGroups library coverage — no SmallGroups id.