Finite Group Databasebeta

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AGL(1,ℤ/8)×#1035 #72275670

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#1035

Splittings

FittingC25×AGL(1,ℤ/8) ⋊ C4
SylowC25 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#1035
commutatorC4×C25C23×C4
FrattiniC4×C5C23×AGL(1,𝔽5)
FittingC25×AGL(1,ℤ/8)C4
socleC2×C5C2×D4×AGL(1,𝔽5)
prime radicalAGL(1,ℤ/8)×D25C2
cosocleC4×D25C24
hypercenterAGL(1,ℤ/8)#1035
hypocenterC25C4×AGL(1,ℤ/8)
LCSG ▷ C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#453×#1035, AGL(1,ℤ/8)×AGL(1,ℤ/25)
maximal normal subgroup of#453×#1035, AGL(1,ℤ/8)×AGL(1,ℤ/25)

GAP

Past the SmallGroups library coverage — no SmallGroups id.