Finite Group Databasebeta

← Prev (#13005788) Next (#13005790) →

C2×D5×#509 #13005789

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D5×#509

Splittings

FittingC2×C5×#509 ⋊ C2
SylowC5 ⋊ C22×#509

Subgroups

subgroupG/H
centerC22C2×D5×D8
commutator, cosocleC5×C8C25
FrattiniC8C24×D5
FittingC2×C5×#509C2
socleC22×C5C22×D8
hypercenterC2×#509D5
hypocenterC5C22×#509
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#509, C2×D5×AGL(1,ℤ/16), C2×D5⋊AGL(1,ℤ/16), …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#509, C2×D5×AGL(1,ℤ/16), C2×D5⋊AGL(1,ℤ/16)
maximal quotient ofC2×C5⋊D5×#509

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1076057);