Finite Group Databasebeta

← Prev (#72254333) Next (#72254335) →

D3×#6399⋊C3 #72254334

order4032
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productD3×#6399⋊C3

Splittings

FittingC3×C7×M16 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#104
SylowC7 ⋊ C3×D3×#104

Subgroups

subgroupG/H
centerC4D3×(C22⋊D7)⋊C3
commutatorC3×C4×C7C22×C3×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽7)
FittingC3×C7×M16C22×C3
socleC2×C3×C7C2×C3×C22⋊C4
prime radicalD3×#1157⋊C3C2
cosocleC2×C3×C4×C7C23×C3
hypercenterM16D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×#104
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#104×AGL(1,𝔽7), D3×#89970⋊C3, D3×#89519⋊C3
maximal normal subgroup ofD3×#104×AGL(1,𝔽7), D3×#89970⋊C3, D3×#89519⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.