Finite Group Databasebeta

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C5×#86711 #14484768

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C28

Aliases

direct productC5×#86711

Splittings

FittingC3×C5×#548 ⋊ C2
HallC3×C5 ⋊ #3480
SylowC3 ⋊ C5×#3480

Subgroups

subgroupG/H
centerC22×C5C24×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC5×#548D3
hypocenterC3C5×#3480
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#548

2224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 210466);