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C5×#68336 #14283299

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68336

Splittings

FittingC3×C5×#328 ⋊ C2
HallC3×C5 ⋊ #1511
SylowC3 ⋊ C5×#1511

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#328D3
hypocenterC3C5×#1511
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#328

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

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, 8997);