Finite Group Databasebeta

C3×#10604735 #14280496

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

Aliases

direct productC3×#10604735

Splittings

HallC3×C5 ⋊ #1451
SylowC5 ⋊ C3×#1451

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×C5C42
cosocleC4×Dic5C23×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#1451
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M16

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6194);