Finite Group Databasebeta

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C3×#66043 #11755720

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

Aliases

direct productC3×#66043

Splittings

FittingC3×C5×#126 ⋊ C2
HallC3×C5 ⋊ #553
SylowC5 ⋊ C3×#553

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#126C2
socleC22×C3×C5C24
hypercenterC3×#126D5
hypocenterC5C3×#553
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#126

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#553, C2×C3×#66043, #14483782, …
maximal normal subgroup ofC3×D5×#553, C2×C3×#66043, #14483782, …
maximal quotient ofC3×#10606693, C3×#10605994, C3×#10607036, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9915);