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C5×#71009 #14292474

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#71009

Splittings

FittingC3×C5×#459 ⋊ C2
HallC3×C5 ⋊ #1687
SylowC3 ⋊ C5×#1687

Subgroups

subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#459C2
socleC22×C3×C5#121
hypercenterC5×#459D3
hypocenterC3C5×#1687
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#459

396 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)(6,7,8)(10,13)(11,16)(14,15)(18,23)(21,24);(7,8)(17,18,22,24,20,23,19,21);(9,10)(11,13)(12,15)(14,16)(18,21)(19,22)(23,24)

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, 18172);