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C5×#71172 #14288278

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

Aliases

direct productC5×#71172

Splittings

FittingC3×C5×#483 ⋊ C2
HallC3×C5 ⋊ #1608
SylowC3 ⋊ C5×#1608

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#483C2
socleC22×C3×C5#120
prime radicalC23×C5×D3D4
hypercenterC5×#483D3
hypocenterC3C5×#1608
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#483

456 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)(17,20)(18,23)(19,25)(21,27)(22,28)(24,30)(26,32)(29,31);(6,7,8)(9,10,12,14)(11,16,15,13)(17,19)(18,22)(20,25)(21,26)(23,28)(24,29)(27,32)(30,31);(10,13)(11,15)(14,16)(17,18,21,24)(19,22,26,29)(20,23,27,30)(25,31,32,28)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 13976);