Finite Group Databasebeta

← Prev (#14289681) Next (#14289683) →

C5×#71236 #14289682

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#71236

Splittings

HallC3×C5 ⋊ #1636
SylowC3 ⋊ C5×#1636

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#487C2
socle, prime radicalC22×C3×C5#120
hypercenterC5×#487D3
hypocenterC3C5×#1636
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#487

376 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)(7,8)(9,12,14,13)(10,16,17,21)(11,19,20,22)(15,23,24,18)(25,28,31,27)(26,32,35,40)(29,37,30,38)(33,39,34,36);(6,7,8)(9,11)(10,15)(12,19)(13,22)(14,20)(16,23)(17,24)(18,21)(25,27,31,28)(26,32,35,40)(29,38,30,37)(33,39,34,36);(9,10,14,17)(11,18,20,23)(12,16,13,21)(15,22,24,19)(25,26,31,35)(27,36,28,39)(29,34,30,33)(32,38,40,37)

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, 15380);