Finite Group Databasebeta

← Prev (#72218494) Next (#72218496) →

AGL(1,𝔽7)×#4078 #72218495

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

Aliases

direct productAGL(1,𝔽7)×#4078

Splittings

FittingC2×C5×C7×D4 ⋊ C22×C3
HallD7×#4078 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C2×AGL(1,ℤ/8)
HallC5×C7 ⋊ C2×C3×AGL(1,ℤ/8)
HallΓL(1,𝔽8) ⋊ C2×#4078
SylowC7 ⋊ C2×C3×#4078
SylowC5 ⋊ AGL(1,ℤ/8)×AGL(1,𝔽7)

Subgroups

subgroupG/H
centerC2C2×C22⋊D5×AGL(1,𝔽7)
commutator, cosocleC4×C5×C7C24×C3
FrattiniC4C22×D5×AGL(1,𝔽7)
FittingC2×C5×C7×D4C22×C3
socleC2×C5×C7C22×C3×D4
hypercenterC2×D4D5×AGL(1,𝔽7)
hypocenterC5×C7C2×C3×AGL(1,ℤ/8)
LCSG ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

1192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

217 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.