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C22×#65487 #12965900

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#65487

Splittings

FittingC22×C5×AGL(1,ℤ/8) ⋊ C2
SylowC5 ⋊ C22×#453

Subgroups

subgroupG/H
centerC23#4083
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×AGL(1,ℤ/8)C2
socleC23×C5#120
hypercenterC22×AGL(1,ℤ/8)D5
hypocenterC5C22×#453
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

5670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1036168);