Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#65529 |
| Hall | C3×C5 ⋊ #410 |
| Sylow | C5 ⋊ C3×#410 |
316 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12)(10,15)(11,17)(13,20)(14,21)(16,19)(18,24)(22,23);(9,11,13,18)(10,14,16,22)(12,17,20,24)(15,21,19,23);(5,6)(7,8)(9,10)(11,14)(12,19,20,15)(13,16)(17,23,24,21)(18,22)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598187, C3×#10598182, #14279086, … |
| maximal normal subgroup of | C3×#10598187, C3×#10598182, #14279086, … |
| maximal quotient of | C3×#10602364, C3×#10602394, C3×#10602417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4332);