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AGL(1,ℤ/8)×D35 #72218472

order2240
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×D35

Splittings

FittingC5×C7×AGL(1,ℤ/8) ⋊ C2
HallC5×C7 ⋊ C2×AGL(1,ℤ/8)
SylowC7 ⋊ D5×AGL(1,ℤ/8)
SylowC5 ⋊ D7×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×D35
commutator, cosocleC4×C5×C7C24
FrattiniC4C23×D35
FittingC5×C7×AGL(1,ℤ/8)C2
socleC2×C5×C7C22×D4
hypercenterAGL(1,ℤ/8)D35
hypocenterC5×C7C2×AGL(1,ℤ/8)
LCSG ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

596 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×C5⋊AGL(1,𝔽7), D5×D7×AGL(1,ℤ/8)
maximal normal subgroup ofAGL(1,ℤ/8)×C5⋊AGL(1,𝔽7), D5×D7×AGL(1,ℤ/8)

GAP

Past the SmallGroups library coverage — no SmallGroups id.