Finite Group Databasebeta

C2×C3×#65057 #14437720

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×C3×#65057

Splittings

HallC3×C5 ⋊ C2×#488
SylowC5 ⋊ C2×C3×#488

Subgroups

subgroupG/H
centerC23×C3D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
hypercenterC2×C3×#102D5
hypocenterC5C2×C3×#488
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 163418);