Finite Group Databasebeta

C3×#10602463 #14302045

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10602463

Splittings

HallC3×C5 ⋊ #1898
SylowC5 ⋊ C3×#1898

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊Dic5
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
Fitting, prime radicalC2×C3×C5×#120C2
socleC22×C3×C5C2×C22⋊C4
cosocleC24×C5C23×C3
hypercenterC2×C3×#120D5
hypocenterC5C3×#1898
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C25×C3 ◁ C2×C3×#120

1196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27743);