Finite Group Databasebeta

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C5×#71199 #14290060

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

Aliases

direct productC5×#71199

Splittings

FittingC3×C5×#486 ⋊ C2
HallC3×C5 ⋊ #1642
SylowC3 ⋊ C5×#1642

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radicalC5×#5718C2
hypercenterC5×#486D3
hypocenterC3C5×#1642
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#486

500 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)(7,8)(10,15)(11,12)(14,16)(17,19,21,20)(18,22,23,24);(6,7,8)(10,14)(11,12)(15,16)(17,18)(19,22)(20,24)(21,23);(9,10,13,16)(11,14,12,15)(18,22)(19,20)(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, 15758);