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B(4,𝔽₂)×AΓL(1,𝔽₉) #72253274

order	9216
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

B(4,𝔽₂)×AΓL(1,𝔽₉)

Splittings

Fitting	C₃²×B(4,𝔽₂) ⋊ SD₁₆
Sylow	C₃² ⋊ SD₁₆×B(4,𝔽₂)

Subgroups

	subgroup	G/H
center	C₂	#120×AΓL(1,𝔽₉)
commutator, cosocle	C₂³×#157	C₂⁵
Frattini	C₂³	C₂³×AΓL(1,𝔽₉)
Fitting	C₃²×B(4,𝔽₂)	SD₁₆
socle	C₂×C₃²	SD₁₆×#120
prime radical	B(4,𝔽₂)×GO⁺(4,𝔽₂)	C₂
hypercenter	B(4,𝔽₂)	AΓL(1,𝔽₉)
hypocenter	C₃²	SD₁₆×B(4,𝔽₂)
LCS	G ▷ C₂³×#157 ▷ C₂×C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ B(4,𝔽₂)

20741 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 72

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

B(4,𝔽₂)×AGL(2,𝔽₃)

GAP

Past the SmallGroups library coverage — no SmallGroups id.