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AGL(1,𝔽7)×#4057 #72218476

order6720
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽7)×#4057

Splittings

FittingC5×C7×D8 ⋊ C22×C3
HallD7×#4057 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C2×AGL(1,ℤ/8)
HallC5×C7 ⋊ C2×C3×AGL(1,ℤ/8)
HallΓL(1,𝔽8) ⋊ C2×#4057
SylowC7 ⋊ C2×C3×#4057
SylowC5 ⋊ AGL(1,ℤ/8)×AGL(1,𝔽7)

Subgroups

subgroupG/H
centerC2D4×D5×AGL(1,𝔽7)
commutator, cosocleC4×C5×C7C24×C3
FrattiniC4C22×D5×AGL(1,𝔽7)
FittingC5×C7×D8C22×C3
socleC2×C5×C7C22×C3×D4
hypercenterD8D5×AGL(1,𝔽7)
hypocenterC5×C7C2×C3×AGL(1,ℤ/8)
LCSG ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C4 ◁ D8

1192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,ℤ/8)×AGL(1,𝔽7)
maximal normal subgroup ofD5×AGL(1,ℤ/8)×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.