Finite Group Databasebeta

← Prev (#72242668) Next (#72242670) →

C2×AGL(1,𝔽5)×#535 #72242669

order2560
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC2×AGL(1,𝔽5)×#535

Splittings

FittingC2×C5×#535 ⋊ C4
SylowC5 ⋊ C2×C4×#535

Subgroups

subgroupG/H
centerC23C24×AGL(1,𝔽5)
commutatorC22×C5C25×C4
FrattiniC22C25×AGL(1,𝔽5)
FittingC2×C5×#535C4
socleC23×C5C24×C4
prime radicalC2×D5×#535C2
cosocleC22×D5C26
hypercenterC2×#535AGL(1,𝔽5)
hypocenterC5C2×C4×#535
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#535

27812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.