Finite Group Databasebeta

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D3×#104×AGL(1,𝔽7) #72254347

order8064
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#104×AGL(1,𝔽7)

Splittings

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

Subgroups

subgroupG/H
centerC4D3×D4×AGL(1,𝔽7)
commutatorC3×C4×C7C23×C3×C4
FrattiniC2×C4C22×D3×AGL(1,𝔽7)
FittingC3×C7×#104C22×C3
socleC2×C3×C7C22×C3×C22⋊C4
prime radicalD3×#41×AGL(1,𝔽7)C2
cosocleC2×C3×C4×C7C24×C3
hypercenter#104D3×AGL(1,𝔽7)
hypocenterC3×C7C22×C3×#104
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

3594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×AGL(1,𝔽7)×#453
maximal normal subgroup ofD3×AGL(1,𝔽7)×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.