Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#4936 |
| Hall | C3×C5 ⋊ #382 |
| Sylow | C3 ⋊ C5×#382 |
308 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(13,15,16,14)(18,22)(21,24);(13,14,16,15)(17,19,20,23)(18,21,22,24);(7,8)(9,10,11,12)(14,15)(17,18)(19,21)(20,22)(23,24)300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#67738, C5×#67713, #14276969, … |
| maximal normal subgroup of | C5×#67738, C5×#67713, #14276969, … |
| maximal quotient of | C5×#71534, C5×#71535, C5×#69412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4630);