Finite Group Databasebeta

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C3×#65935 #11755612

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

Aliases

direct productC3×#65935

Splittings

FittingC3×C5×#121 ⋊ C2
HallC3×C5 ⋊ #553
SylowC5 ⋊ C3×#553

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#121C2
socleC22×C3×C5C24
hypercenterC3×#121D5
hypocenterC5C3×#553
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#121

476 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)(11,16)(13,15)(17,19)(18,22)(20,23)(21,24);(9,11,12,16)(10,13,14,15)(18,21)(19,23);(19,23)(22,24);(5,6)(7,8)(9,10,12,14)(11,15,16,13)(17,18,20,21)(19,22,23,24)

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#553, C2×C3×#65935, #14483626, …
maximal normal subgroup ofC3×D5×#553, C2×C3×#65935, #14483626, …
maximal quotient ofC3×#10605611, C3×#10607205, C3×#10606404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9807);