Finite Group Databasebeta

C2×#11756298 #14483804

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

Aliases

direct productC2×#11756298

Splittings

HallC3×C5 ⋊ C2×#554
SylowC5 ⋊ C2×#5539
SylowC3 ⋊ C2×#65873

Subgroups

subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×C4×D4D15
hypocenterC3×C5C2×#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

2400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 209502);