Finite Group Databasebeta

C2×C5×#5603 #14481310

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C28

Aliases

direct productC2×C5×#5603

Splittings

HallC3×C5 ⋊ C2×#542
SylowC3 ⋊ C2×C5×#542

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
Fitting, prime radicalC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×C5×#121D3
hypocenterC3C2×C5×#542
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#121

2264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 207008);