Finite Group Databasebeta

← Prev (#14479652) Next (#14479654) →

C22×C5×#885 #14479653

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×C5×#885

Splittings

FittingC22×C3×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ C22×#124
SylowC3 ⋊ C22×C5×#124

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C5×#67C2
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C22×C5×#124
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C22⋊C4

3760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 205351);