Finite Group Databasebeta

C2×C5×#4648 #14319349

order1920
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×C5×#4648

Splittings

HallC3×C5 ⋊ C2×#376
SylowC3 ⋊ C2×C5×#376

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutatorC2×C3C22×C42×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC2×C5×#95D3
hypocenterC3C2×C5×#376
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C2×C5×#95

1680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

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, 45047);