Finite Group Databasebeta

← Prev (#72244268) Next (#72244270) →

D3×D7×#99 #72244269

order2688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×D7×#99

Splittings

FittingC3×C7×#99 ⋊ C22
HallC3×C7 ⋊ C22×#99
SylowC7 ⋊ C2×D3×#99
SylowC3 ⋊ C2×D7×#99

Subgroups

subgroupG/H
centerC2D3×D7×C22⋊C4
commutatorC22×C3×C7C23×C4
FrattiniC23C22×D3×D7
FittingC3×C7×#99C22
socleC2×C3×C7C22×C22⋊C4
prime radicalC2×D3×D4×D7C2
cosocleC23×C3×C7C24
hypercenter#99D3×D7
hypocenterC3×C7C22×#99
LCSG ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C23 ◁ #99

2224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D7×B(4,𝔽2), D3×#99×AGL(1,𝔽7)
maximal normal subgroup ofD3×D7×B(4,𝔽2), D3×#99×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.