Finite Group Databasebeta

C2×C3×#65851 #14480115

order1920
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28

Aliases

direct productC2×C3×#65851

Splittings

HallC3×C5 ⋊ C2×#533
SylowC5 ⋊ C2×C3×#533

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C3×#117D5
hypocenterC5C2×C3×#533
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×#117

2336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 205813);