Finite Group Databasebeta

C3×#10598302 #14278698

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10598302

Splittings

HallC3×C5 ⋊ #1375
SylowC5 ⋊ C3×#1375

Subgroups

subgroupG/H
centerC2×C3×C4C4×Dic5
commutatorC4×C5C3×C4×C8
FrattiniC22×C8C2×C3×D5
FittingC2×C3×C5×M32C2
socleC22×C3×C5#97
prime radicalC23×C3×C5M16
cosocleC22×C5×C8C22×C3
hypercenterC2×C3×M32D5
hypocenterC5C3×#1375
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M32

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4396);