Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#5088 |
| Fitting | C3×C5×C4⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #486 |
| Sylow | C3 ⋊ C5×#486 |
236 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 94 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)(9,11,12,16)(10,14,13,15)(18,21)(19,24)(22,23);(9,10,12,13)(11,15,16,14);(7,8)(10,13)(14,15)(17,18)(19,21)(20,23)(22,24)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71910, C5×#68432, #14289112, … |
| maximal normal subgroup of | C5×#71910, C5×#68432, #14289112, … |
| maximal quotient of | C5×#69574, C5×#69615, C5×#69580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4782);