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C4×#65490 #12105192

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#65490

Splittings

FittingC4×C5×AGL(1,ℤ/8) ⋊ C2
SylowC5 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#4083
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×AGL(1,ℤ/8)C2
socleC22×C5C2×#120
prime radicalC2×#65490C2
cosocleC22×C4×C5C24
hypercenterC4×AGL(1,ℤ/8)D5
hypocenterC5C4×#454
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 175460);