Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5034 |
| Hall | C3×C5 ⋊ #481 |
| Sylow | C3 ⋊ C5×#481 |
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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)(6,7,8)(11,15)(13,16)(18,21)(19,24)(22,23);(9,11)(10,13)(12,15)(14,16);(7,8)(9,10,12,14)(11,13,15,16)(17,18,20,23)(19,21,24,22)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71844, C5×#68290, #14288539, … |
| maximal normal subgroup of | C5×#71844, C5×#68290, #14288539, … |
| maximal quotient of | C5×#69502, C5×#69505, C5×#71677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4728);