Finite Group Databasebeta

← Prev (#14412155) Next (#14412157) →

C3×#10610428 #14412156

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10610428

Splittings

FittingC2×C3×C5×#100 ⋊ C2
HallC3×C5 ⋊ #2888
SylowC5 ⋊ C3×#2888

Subgroups

subgroupG/H
centerC2×C3C2×D5×C22⋊C4
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#100C2
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×#4144C2
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#100D5
hypocenterC5C3×#2888
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137854);