Finite Group Databasebeta

C2×#11751050 #14331999

order1920
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11751050

Splittings

HallC3×C5 ⋊ C2×#399
SylowC5 ⋊ C2×#4949
SylowC3 ⋊ C2×#65238

Subgroups

subgroupG/H
centerC24C22×D15
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC25×C3×C5C22
hypercenterC22×C22⋊C4D15
hypocenterC3×C5C2×#399
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 57697);