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C5×#71209 #14292156

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

Aliases

direct productC5×#71209

Splittings

HallC3×C5 ⋊ #1682
SylowC3 ⋊ C5×#1682

Subgroups

subgroupG/H
centerC22×C5#938
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#486C2
socleC22×C3×C5#121
prime radicalC3×C5×#127C22
hypercenterC5×#486D3
hypocenterC3C5×#1682
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#486

332 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)(17,19,20,26)(18,23,22,31)(21,30,28,27)(24,32,29,25);(6,7,8)(9,10,14,16,12,15,11,13)(18,22)(23,31)(24,29)(25,32);(10,13)(11,14)(15,16)(17,18)(19,25)(20,22)(21,29)(23,27)(24,28)(26,32)(30,31)

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, 17854);