Finite Group Databasebeta

← Prev (#14293358) Next (#14293360) →

C5×#70967 #14293359

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

Aliases

direct productC5×#70967

Splittings

HallC3×C5 ⋊ #1704
SylowC3 ⋊ C5×#1704

Subgroups

subgroupG/H
centerC22×C5#930
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#446C2
socle, prime radicalC22×C3×C5#121
hypercenterC5×#446D3
hypocenterC3C5×#1704
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#446

280 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)(6,7,8)(11,19)(14,23)(17,24)(20,22)(25,27,28,34)(26,31,30,39)(29,38,36,35)(32,40,37,33);(9,11,18,22,13,19,12,20)(10,14,21,24,16,23,15,17)(26,30)(31,39)(32,37)(33,40);(7,8)(9,10,13,16)(11,17,19,24)(12,21,18,15)(14,22,23,20)(25,26)(27,33)(28,30)(29,37)(31,35)(32,36)(34,40)(38,39)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19057);