Finite Group Databasebeta

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C5×#68456 #14289160

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

Aliases

direct productC5×#68456

Splittings

FittingC3×C5×#332 ⋊ C2
HallC3×C5 ⋊ #1626
SylowC3 ⋊ C5×#1626

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC5×#332D3
hypocenterC3C5×#1626
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#332

420 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)(9,11,13,12)(10,14,15,16)(17,19,21,18)(20,22,24,23);(9,10)(11,14)(12,16)(13,15)(17,18,21,19)(20,23,24,22);(7,8)(10,14)(11,12)(15,16)(18,22)(19,23)(20,24)

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, 14858);