Finite Group Databasebeta

C3×#10614311 #14330638

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C22×C42

Aliases

direct productC3×#10614311

Splittings

HallC3×C5 ⋊ #2375
SylowC5 ⋊ C3×#2375

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
Fitting, prime radicalC2×C3×C5×#120C2
socleC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC2×C3×#120D5
hypocenterC5C3×#2375
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

1376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 56336);