Finite Group Databasebeta

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C5×#5681 #11756066

order960
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#5681

Splittings

FittingC3×C5×#124 ⋊ C2
HallC3×C5 ⋊ #559
SylowC3 ⋊ C5×#559

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×#124C2
socleC22×C3×C5C24
prime radicalC5×#940C2
hypercenterC5×#124D3
hypocenterC3C5×#559
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#124

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80517, C5×#81633, #14471776, …
maximal normal subgroup ofC5×#80517, C5×#81633, #14471776, …
maximal quotient ofC5×#74158, C5×#76489, C5×#75476, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10261);