Finite Group Databasebeta

C2×C5×#5517 #14480114

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

Aliases

direct productC2×C5×#5517

Splittings

HallC3×C5 ⋊ C2×#533
SylowC3 ⋊ C2×C5×#533

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C5×#117D3
hypocenterC3C2×C5×#533
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C2×C5×#117

2336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 205812);