Finite Group Databasebeta

← Prev (#72254395) Next (#72254397) →

D3×#6380⋊C3 #72254396

order4032
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productD3×#6380⋊C3

Splittings

FittingC3×C7×C22⋊C4 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#99
SylowC7 ⋊ C3×D3×#99

Subgroups

subgroupG/H
centerC2D3×(C2×AGL(1,𝔽7))⋊C4
commutatorC22×C3×C7C22×C3×C4
FrattiniC23C2×D3×AGL(1,𝔽7)
FittingC3×C7×C22⋊C4C22×C3
socleC2×C3×C7C2×C3×C22⋊C4
prime radicalC2×D3×(C22⋊D7)⋊C3C2
cosocleC23×C3×C7C23×C3
hypercenterC22⋊C4D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×#99
LCSG ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C23 ◁ C22⋊C4

892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#99×AGL(1,𝔽7), D3×#89804⋊C3, D3×#89513⋊C3
maximal normal subgroup ofD3×#99×AGL(1,𝔽7), D3×#89804⋊C3, D3×#89513⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.