Finite Group Databasebeta

← Prev (#11755731) Next (#11755733) →

C3×#66055 #11755732

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

Aliases

direct productC3×#66055

Splittings

HallC3×C5 ⋊ #557
SylowC5 ⋊ C3×#557

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C4⋊Q8C2
socle, prime radicalC22×C3×C5C24
hypercenterC3×C4⋊Q8D5
hypocenterC5C3×#557
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10601997, C3×#10599249, #14289175, …
maximal normal subgroup ofC3×#10601997, C3×#10599249, #14289175, …
maximal quotient ofC3×#10606054, C3×#10607713, C3×#10608220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9927);