Finite Group Databasebeta

← Prev (#14288106) Next (#14288108) →

C5×#68295 #14288107

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68295

Splittings

FittingC3×C5×#327 ⋊ C2
HallC3×C5 ⋊ #1604
SylowC3 ⋊ C5×#1604

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radicalC5×#5597C2
hypercenterC5×#327D3
hypocenterC3C5×#1604
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#327

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7)(9,11,12,15)(10,13,14,16);(9,10)(11,13)(12,14)(15,16)(18,21)(19,24)(22,23);(7,8)(13,16)(17,18,20,23)(19,21,24,22)

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, 13805);