Finite Group Databasebeta

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C5×#71206 #14289934

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

Aliases

direct productC5×#71206

Splittings

HallC3×C5 ⋊ #1640
SylowC3 ⋊ C5×#1640

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenterC5×#486D3
hypocenterC3C5×#1640
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#486

424 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)(7,8)(9,11,13,12)(10,14,15,16)(17,19)(18,22)(20,30)(21,26)(23,32)(24,31)(25,28)(27,29);(6,7,8)(9,10)(11,14)(12,16)(13,15)(20,29)(23,28)(25,32)(27,30);(10,14)(11,12)(15,16)(17,18,21,24)(19,25,26,32)(20,28,29,23)(22,30,31,27)

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, 15632);