Finite Group Databasebeta

C2×C5×#5153 #14425923

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#5153

Splittings

HallC3×C5 ⋊ C2×#463
SylowC3 ⋊ C2×C5×#463

Subgroups

subgroupG/H
centerC23×C5D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC22×C3×C5×D8C2
socleC23×C3×C5C2×D4
hypercenterC22×C5×D8D3
hypocenterC3C2×C5×#463
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C4×C5 ◁ C22×C5×D8

1128 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, 151621);