Finite Group Databasebeta

C2×C5×#5247 #14319802

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C29

Aliases

direct productC2×C5×#5247

Splittings

HallC3×C5 ⋊ C2×#379
SylowC3 ⋊ C2×C5×#379

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC26×C3×C5C2
socleC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC26×C5D3
hypocenterC3C2×C5×#379
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C26×C5

6928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45500);