Finite Group Databasebeta

← Prev (#14478493) Next (#14478495) →

C5×#82036 #14478494

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#82036

Splittings

FittingC3×C5×#509 ⋊ C2
HallC3×C5 ⋊ #3415
SylowC3 ⋊ C5×#3415

Subgroups

subgroupG/H
centerC2×C5C2×D3×D8
commutator, cosocleC3×C8C24×C5
FrattiniC8C23×C5×D3
FittingC3×C5×#509C2
socleC2×C3×C5C22×D8
hypercenterC5×#509D3
hypocenterC3C5×#3415
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#509

740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 40 points:

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

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, 204192);