Finite Group Databasebeta

← Prev (#72244278) Next (#72244280) →

D3×D7×#100 #72244279

order2688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×D7×#100

Splittings

FittingC3×C7×#100 ⋊ C22
HallC3×C7 ⋊ C22×#100
SylowC7 ⋊ C2×D3×#100
SylowC3 ⋊ C2×D7×#100

Subgroups

subgroupG/H
centerC2D3×D7×C22⋊C4
commutatorC22×C3×C7C23×C4
FrattiniC2×C4C22×D3×D7
FittingC3×C7×#100C22
socleC2×C3×C7C22×C22⋊C4
prime radicalC2×D3×D4×D7C2
cosocleC2×C3×C4×C7C24
hypercenter#100D3×D7
hypocenterC3×C7C22×#100
LCSG ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

1984 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×#453, D3×#100×AGL(1,𝔽7), D7×#10591503
maximal normal subgroup ofD3×D7×#453, D3×#100×AGL(1,𝔽7)
maximal quotient ofD7×#10591503

GAP

Past the SmallGroups library coverage — no SmallGroups id.