Finite Group Databasebeta

← Prev (#14320131) Next (#14320133) →

D5×#4975 #14320132

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD5×#4975

Splittings

HallC3×C5 ⋊ C2×#384
SylowC5 ⋊ C2×#4975
SylowC3 ⋊ D5×#384

Subgroups

subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#384
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

1776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45830);