Finite Group Databasebeta

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SD₁₆×GL(3,𝔽₂) #72220597

order	2688
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

SD₁₆×GL(3,𝔽₂)

Subgroups

	subgroup	G/H
center	C₂	D₄×GL(3,𝔽₂)
commutator	C₄×GL(3,𝔽₂)	C₂²
Frattini, cosocle	C₄	C₂²×GL(3,𝔽₂)
Fitting, hypercenter	SD₁₆	GL(3,𝔽₂)
socle	C₂×GL(3,𝔽₂)	D₄
prime radical	D₄×GL(3,𝔽₂)	C₂
hypocenter	GL(3,𝔽₂)	SD₁₆
LCS	G ▷ C₄×GL(3,𝔽₂) ▷ C₂×GL(3,𝔽₂) ▷ GL(3,𝔽₂)
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

319 conjugacy classes of subgroups; only the 14 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 14 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

42 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

GL(2,𝔽₃)×GL(3,𝔽₂)

GAP

Past the SmallGroups library coverage — no SmallGroups id.