Finite Group Databasebeta

← Prev (#11755634) Next (#11755636) →

C3×#65958 #11755635

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#65958

Splittings

FittingC3×C5×C22⋊Q8 ⋊ C2
HallC3×C5 ⋊ #529
SylowC5 ⋊ C3×#529

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C22⋊Q8C2
socleC22×C3×C5C24
prime radicalC3×#4076C2
hypercenterC3×C22⋊Q8D5
hypocenterC5C3×#529
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊Q8

468 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)(4,5,7,8,6)(9,11,12,15)(10,13,14,16)(18,22)(21,24);(11,15)(13,16)(17,19,20,23)(18,21,22,24);(11,15)(13,16)(17,18)(19,21)(20,22)(23,24);(5,6)(7,8)(9,10,12,14)(11,13,15,16)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10604510, #14281870, C3×#10604511, …
maximal normal subgroup ofC3×#10604510, #14281870, C3×#10604511, …
maximal quotient ofC3×#10605594, C3×#10606108, C3×#10607692, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9830);