Finite Group Databasebeta

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C5×#68464 #14291358

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

Aliases

direct productC5×#68464

Splittings

FittingC3×C5×#332 ⋊ C2
HallC3×C5 ⋊ #1666
SylowC3 ⋊ C5×#1666

Subgroups

subgroupG/H
centerC22×C5#884
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#332C2
socleC22×C3×C5#121
prime radicalC5×#874C22
hypercenterC5×#332D3
hypocenterC3C5×#1666
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#332

344 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)(17,18,20,22)(19,24,23,21);(7,8)(9,10,11,13,12,14,15,16);(7,8)(10,13)(11,15)(14,16)(18,21)(19,23)(22,24)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 17056);