Finite Group Databasebeta

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D3×#67×AGL(1,𝔽7) #72247044

order6048
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productD3×#67×AGL(1,𝔽7)

Splittings

FittingC22×C32×C7 ⋊ C23×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×D4
SylowC7 ⋊ C2×C3×D3×#67

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽7)
commutator, socle, cosocleC2×C32×C7C24×C3
FittingC22×C32×C7C23×C3
hypercenterC22D32×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C22

2436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×D4×AGL(1,𝔽7)
maximal normal subgroup ofD32×D4×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.