Finite Group Databasebeta

← Prev (#72259200) Next (#72259202) →

B(4,𝔽₂)×D₁₃⋊C₃ #72259201

order	4992
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁷

Aliases

B(4,𝔽₂)×D₁₃⋊C₃

Splittings

Fitting	C₁₃×B(4,𝔽₂) ⋊ C₂×C₃
Hall	D₁₃×B(4,𝔽₂) ⋊ C₃
Hall	C₁₃⋊C₃ ⋊ C₂×B(4,𝔽₂)
Sylow	C₁₃ ⋊ C₂×C₃×B(4,𝔽₂)

Subgroups

	subgroup	G/H
center	C₂	#120×D₁₃⋊C₃
commutator, cosocle	C₂³×C₁₃	C₂⁴×C₃
Frattini	C₂³	C₂³×D₁₃⋊C₃
Fitting	C₁₃×B(4,𝔽₂)	C₂×C₃
socle	C₂×C₁₃	C₂×C₃×#120
hypercenter	B(4,𝔽₂)	D₁₃⋊C₃
hypocenter	C₁₃	C₂×C₃×B(4,𝔽₂)
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ B(4,𝔽₂)

2036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 104

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	B(4,𝔽₂)×AGL(1,𝔽₁₃), D₁₃⋊C₃×#5934
maximal normal subgroup of	B(4,𝔽₂)×AGL(1,𝔽₁₃)

GAP

Past the SmallGroups library coverage — no SmallGroups id.