Finite Group Databasebeta

← Prev (#14298589) Next (#14298591) →

C3×#10604158 #14298590

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10604158

Splittings

FittingC2×C3×C42×C5 ⋊ C4
HallC3×C5 ⋊ #1827
SylowC5 ⋊ C3×#1827

Subgroups

subgroupG/H
centerC3×C4#4130
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socleC2×C3×C5#381
prime radicalC2×C3×#709C22
cosocleC2×C4×D5C23×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C3×#1827
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C3×C42 ◁ C2×C3×C42

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24288);