Finite Group Databasebeta

← Prev (#14292299) Next (#14292301) →

C5×#68511 #14292300

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#68511

Splittings

HallC3×C5 ⋊ #1684
SylowC3 ⋊ C5×#1684

Subgroups

subgroupG/H
centerC22×C5#884
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#333C2
socle, prime radicalC22×C3×C5#121
hypercenterC5×#333D3
hypocenterC3C5×#1684
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#333

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7)(25,27,28,34)(26,31,30,39)(29,38,36,35)(32,40,37,33);(7,8)(9,11,18,22,13,20,12,19)(10,14,21,24,16,23,15,17)(26,30)(31,39)(32,37)(33,40);(7,8)(9,10,13,16)(11,17,20,24)(12,21,18,15)(14,22,23,19)(25,26)(27,33)(28,30)(29,37)(31,35)(32,36)(34,40)(38,39)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 17998);