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D3×AGL(1,ℤ/8)×AGL(1,𝔽7) #72245690

order8064
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productD3×AGL(1,ℤ/8)×AGL(1,𝔽7)

Splittings

FittingC3×C7×AGL(1,ℤ/8) ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C22×AGL(1,ℤ/8)
SylowC7 ⋊ C2×C3×D3×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D3×D4×AGL(1,𝔽7)
commutator, cosocleC3×C4×C7C25×C3
FrattiniC4C23×D3×AGL(1,𝔽7)
FittingC3×C7×AGL(1,ℤ/8)C22×C3
socleC2×C3×C7C23×C3×D4
hypercenterAGL(1,ℤ/8)D3×AGL(1,𝔽7)
hypocenterC3×C7C22×C3×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

7178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽7)×#453
maximal normal subgroup ofD3×AGL(1,𝔽7)×#453
holomorph ofC3×C7×C8

GAP

Past the SmallGroups library coverage — no SmallGroups id.