Finite Group Databasebeta

C3×#10602238 #14313972

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10602238

Splittings

HallC3×C5 ⋊ #2141
SylowC5 ⋊ C3×#2141

Subgroups

subgroupG/H
centerC22×C3C2×D40
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×M32C2
socleC22×C3×C5C2×D8
prime radicalC23×C3×C5D8
cosocleC2×C5×C8C23×C3
hypercenterC2×C3×M32D5
hypocenterC5C3×#2141
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×M32

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39670);