Finite Group Databasebeta

C3×#10603979 #14287331

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#10603979

Splittings

HallC3×C5 ⋊ #1590
SylowC5 ⋊ C3×#1590

Subgroups

subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#103C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D20C2×C4
cosocleC4×Dic5C23×C3
hypercenterC3×#103AGL(1,𝔽5)
hypocenterC5C3×#1590
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 13029);