Finite Group Databasebeta

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C2×D5×AGL(1,ℤ/16) #72242365

order2560
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×D5×AGL(1,ℤ/16)

Splittings

FittingC2×C5×AGL(1,ℤ/16) ⋊ C2
SylowC5 ⋊ C22×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22D5×#442
commutatorC5×C8C24×C4
FrattiniC2×C8C24×D5
FittingC2×C5×AGL(1,ℤ/16)C2
socleC22×C5C2×#442
prime radicalC2×D5×#509C2
cosocleC2×C5×C8C25
hypercenterC2×AGL(1,ℤ/16)D5
hypocenterC5C22×AGL(1,ℤ/16)
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×AGL(1,ℤ/16)

4268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×AGL(1,ℤ/16)
maximal normal subgroup ofC2×AGL(1,𝔽5)×AGL(1,ℤ/16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.