Finite Group Databasebeta

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C5×#71149 #14291805

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

Aliases

direct productC5×#71149

Splittings

HallC3×C5 ⋊ #1676
SylowC3 ⋊ C5×#1676

Subgroups

subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#477C2
socle, prime radicalC22×C3×C5#121
hypercenterC5×#477D3
hypocenterC3C5×#1676
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#477

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

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, 17503);