Finite Group Databasebeta

← Prev (#14418482) Next (#14418484) →

C3×#10617374 #14418483

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10617374

Splittings

HallC3×C5 ⋊ #2960
SylowC5 ⋊ C3×#2960

Subgroups

subgroupG/H
centerC22×C3C23×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C23×C4
prime radicalC22×C3×D5C22×C4
cosocleC2×Dic5C24×C3
hypercenterC3×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C3×#2960
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 144181);