Finite Group Databasebeta

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SD₁₆×AGL(2,𝔽₃) #72220178

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

Aliases

SD₁₆×AGL(2,𝔽₃)

Splittings

C₃²×SD₁₆ ⋊ GL(2,𝔽₃)

Subgroups

	subgroup	G/H
center	C₂	D₄×AGL(2,𝔽₃)
commutator, cosocle	C₄×PSU(3,𝔽₂)⋊C₃	C₂³
Frattini	C₄	C₂²×AGL(2,𝔽₃)
Fitting	C₃²×SD₁₆	GL(2,𝔽₃)
socle	C₂×C₃²	D₄×GL(2,𝔽₃)
prime radical	D₄×AGL(2,𝔽₃)	C₂
hypercenter	SD₁₆	AGL(2,𝔽₃)
hypocenter	PSU(3,𝔽₂)⋊C₃	C₂×SD₁₆
LCS	G ▷ C₄×PSU(3,𝔽₂)⋊C₃ ▷ C₂×PSU(3,𝔽₂)⋊C₃ ▷ PSU(3,𝔽₂)⋊C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

1354 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.