Finite Group Databasebeta

← Prev (#72247041) Next (#72247043) →

D3×D4×C3⋊AGL(1,𝔽7) #72247042

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

Aliases

direct productD3×D4×C3⋊AGL(1,𝔽7)

Splittings

FittingC32×C7×D4 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×D4
SylowC7 ⋊ C3×D32×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×D3×C3⋊AGL(1,𝔽7)
commutator, socle, cosocleC2×C32×C7C24×C3
FittingC32×C7×D4C22×C3
hypercenterD4D3×C3⋊AGL(1,𝔽7)
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ D4

2244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

180 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.