Finite Group Databasebeta

← Prev (#14290377) Next (#14290379) →

C5×#71048 #14290378

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

Aliases

direct productC5×#71048

Splittings

FittingC3×C5×#461 ⋊ C2
HallC3×C5 ⋊ #1647
SylowC3 ⋊ C5×#1647

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#461C2
socleC22×C3×C5#120
prime radicalC5×#5555C2
hypercenterC5×#461D3
hypocenterC3C5×#1647
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#461

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 16076);