Finite Group Databasebeta

C2×C5×#5912 #14511408

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC2×C5×#5912

Splittings

FittingC24×C4×C5 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4×C5C2×S4
commutator, cosocleC2×A4C24×C5
FrattiniC2C23×C5×S4
FittingC24×C4×C5D3
socleC24×C5C22×D3
hypercenterC22×C4×C5S4
hypocenterA4C2×C5×#41
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237106);