Finite Group Databasebeta

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D3×D7×#104 #72244341

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

Aliases

direct productD3×D7×#104

Splittings

FittingC3×C7×#104 ⋊ C22
HallC3×C7 ⋊ C22×#104
SylowC7 ⋊ C2×D3×#104
SylowC3 ⋊ C2×D7×#104

Subgroups

subgroupG/H
centerC4D3×D4×D7
commutatorC3×C4×C7C23×C4
FrattiniC2×C4C22×D3×D7
FittingC3×C7×#104C22
socleC2×C3×C7C22×C22⋊C4
prime radicalD3×D7×#41C2
cosocleC2×C3×C4×C7C24
hypercenter#104D3×D7
hypocenterC3×C7C22×#104
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

1712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D7×#453, D7×#10590393, D3×#104×AGL(1,𝔽7)
maximal normal subgroup ofD3×D7×#453, D3×#104×AGL(1,𝔽7)
maximal quotient ofD7×#10590393

GAP

Past the SmallGroups library coverage — no SmallGroups id.