Finite Group Databasebeta

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C5×#68446 #14292111

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

Aliases

direct productC5×#68446

Splittings

FittingC3×C5×#332 ⋊ C2
HallC3×C5 ⋊ #1681
SylowC3 ⋊ C5×#1681

Subgroups

subgroupG/H
centerC22×C5#884
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#332C2
socleC22×C3×C5#121
prime radicalC5×#4843C2
hypercenterC5×#332D3
hypocenterC3C5×#1681
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#332

364 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)(10,14)(12,16)(13,15);(7,8)(10,13)(14,15)(17,18,22,24,20,23,19,21);(7,8)(9,10)(11,13)(12,14)(15,16)(18,21)(19,22)(23,24)

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, 17809);