Finite Group Databasebeta

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AGL(1,ℤ/8)×#1044 #72220907

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5

Aliases

direct productAGL(1,ℤ/8)×#1044

Splittings

FittingC52×AGL(1,ℤ/8) ⋊ C4
SylowC52 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#1044
commutatorC4×C52C23×C4
FrattiniC4C23×#1044
FittingC52×AGL(1,ℤ/8)C4
socleC2×C52C2×C4×D4
prime radicalAGL(1,ℤ/8)×C5⋊D5C2
cosocleC4×C5⋊D5C24
hypercenterAGL(1,ℤ/8)#1044
hypocenterC52C4×AGL(1,ℤ/8)
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

1394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×D5⋊AGL(1,𝔽5), #72223001, #72223005, …
maximal normal subgroup ofAGL(1,ℤ/8)×D5⋊AGL(1,𝔽5), #72223001, #72223005, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.