Finite Group Databasebeta

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D52×AGL(1,ℤ/8) #72220848

order3200
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD52×AGL(1,ℤ/8)

Splittings

FittingC52×AGL(1,ℤ/8) ⋊ C22
SylowC52 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×D52
commutator, cosocleC4×C52C25
FrattiniC4C23×D52
FittingC52×AGL(1,ℤ/8)C22
socleC2×C52C23×D4
hypercenterAGL(1,ℤ/8)D52
hypocenterC52C22×AGL(1,ℤ/8)
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

3738 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221406, AGL(1,ℤ/8)×D5⋊AGL(1,𝔽5), #72223001
maximal normal subgroup of#72221406, AGL(1,ℤ/8)×D5⋊AGL(1,𝔽5), #72223001

GAP

Past the SmallGroups library coverage — no SmallGroups id.