Finite Group Databasebeta

C3×#10602442 #14301439

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10602442

Splittings

HallC3×C5 ⋊ #1885
SylowC5 ⋊ C3×#1885

Subgroups

subgroupG/H
centerC22×C3#4099
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#518C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#518D5
hypocenterC5C3×#1885
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#518

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 27137);