Finite Group Databasebeta

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C3×#65991 #11755668

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

Aliases

direct productC3×#65991

Splittings

FittingC3×C5×#123 ⋊ C2
HallC3×C5 ⋊ #538
SylowC5 ⋊ C3×#538

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#123C2
socleC22×C3×C5C24
hypercenterC3×#123D5
hypocenterC5C3×#538
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#123

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#538, C2×C3×#65991, #14480783, …
maximal normal subgroup ofC3×D5×#538, C2×C3×#65991, #14480783, …
maximal quotient ofC3×#10607556, C3×#10605851, C3×#10606676, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9863);