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C5×#71200 #14291841

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

Aliases

direct productC5×#71200

Splittings

FittingC3×C5×#486 ⋊ C2
HallC3×C5 ⋊ #1677
SylowC3 ⋊ C5×#1677

Subgroups

subgroupG/H
centerC22×C5#938
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#486C2
socleC22×C3×C5#121
prime radicalC5×#5072C2
hypercenterC5×#486D3
hypocenterC3C5×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#486

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(7,8)(10,14)(12,16)(13,15);(6,7,8)(10,13)(14,15)(17,18,19,21,20,22,23,24);(9,10)(11,13)(12,14)(15,16)(18,21)(19,23)(22,24)

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, 17539);