Finite Group Databasebeta

C2×#11750860 #14429810

order1920
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11750860

Splittings

HallC3×C5 ⋊ C2×#474
SylowC5 ⋊ C2×#4759
SylowC3 ⋊ C2×#65048

Subgroups

subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
hypercenterC2×#102D15
hypocenterC3×C5C2×#474
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 155508);