Finite Group Databasebeta

C2×C3×#64782 #14313783

order1920
isoclinismisoclinic class of #3958
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×#64782

Splittings

HallC3×C5 ⋊ C2×#357
SylowC5 ⋊ C2×C3×#357

Subgroups

subgroupG/H
centerC23×C3#686
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
Fitting, prime radicalC22×C3×C5×D8C2
socleC23×C3×C5D8
cosocleC2×C5×C8C23×C3
hypercenterC22×C3×D8D5
hypocenterC5C2×C3×#357
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C22×C3×D8

544 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, 39481);