Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C4 |
| direct product | C3×#65360 |
| Hall | C3×C5 ⋊ #490 |
| Sylow | C5 ⋊ C3×#490 |
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(11,15)(18,22)(19,24)(21,23);(9,11,12,15)(10,13,14,16)(18,21)(22,23);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,19,23,20,21,24,22)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598746, #14278354, C3×#10598030, … |
| maximal normal subgroup of | C3×#10598746, #14278354, C3×#10598030, … |
| maximal quotient of | C3×#10600368, C3×#10600438, C3×#10602558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4163);