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AGL(1,ℤ/8)×#64425 #72245272

order9408
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C7

Aliases

direct productAGL(1,ℤ/8)×#64425

Splittings

FittingC72×AGL(1,ℤ/8) ⋊ C2×C3
HallAGL(1,ℤ/8)×C7⋊D7 ⋊ C3
Hall#3862 ⋊ C2×AGL(1,ℤ/8)
SylowC72 ⋊ C2×C3×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#64425
commutator, cosocleC4×C72C24×C3
FrattiniC4C23×#64425
FittingC72×AGL(1,ℤ/8)C2×C3
socleC2×C72C22×C3×D4
hypercenterAGL(1,ℤ/8)#64425
hypocenterC72C2×C3×AGL(1,ℤ/8)
LCSG ▷ C4×C72 ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #453×#64425
maximal normal subgroup ofAGL(1,ℤ/8)×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #453×#64425

GAP

Past the SmallGroups library coverage — no SmallGroups id.