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C22×#66109 #13013118

order1280
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#66109

Splittings

FittingC22×C5×AGL(1,ℤ/8) ⋊ C2
SylowC5 ⋊ C22×#577

Subgroups

subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC4×C5C26
FrattiniC4C25×D5
FittingC22×C5×AGL(1,ℤ/8)C2
socleC23×C5C22×D4
hypercenterC22×AGL(1,ℤ/8)D5
hypocenterC5C22×#577
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

11118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1083386);