Finite Group Databasebeta

C3×#10598211 #14278876

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

Aliases

direct productC3×#10598211

Splittings

HallC3×C5 ⋊ #1383
SylowC5 ⋊ C3×#1383

Subgroups

subgroupG/H
centerC22×C3#3940
commutatorC5×C8C3×C42
FrattiniC22×C8C2×C3×D5
FittingC2×C3×C5×#106C2
socleC22×C3×C5#106
prime radicalC23×C3×C5SD16
cosocleC22×C5×C8C22×C3
hypercenterC2×C3×#106D5
hypocenterC5C3×#1383
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#106

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 4574);