Finite Group Databasebeta

C3×#10602218 #14312750

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10602218

Splittings

HallC3×C5 ⋊ #2110
SylowC5 ⋊ C3×#2110

Subgroups

subgroupG/H
centerC3×C8C4×Dic5
commutatorC4×C5C2×C3×C42
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×M32C2
socleC2×C3×C5C2×#97
prime radicalC23×C3×C5M16
cosocleC2×C5×C8C23×C3
hypercenterC2×C3×M32D5
hypocenterC5C3×#2110
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C3×C8 ◁ C2×C3×M32

320 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, 38448);