Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5193 |
| Fitting | C3×C5×#135 ⋊ C2 |
| Hall | C3×C5 ⋊ #509 |
| Sylow | C3 ⋊ C5×#509 |
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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)(6,7,8)(9,10)(11,18)(12,21)(13,15)(14,17)(16,19)(20,23)(22,24);(10,15)(14,22)(16,21)(18,23);(7,8)(10,14)(11,17)(12,19)(15,22)(16,23)(18,21)(20,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#69249, C5×#70929, #14315872, … |
| maximal normal subgroup of | C5×#69249, C5×#70929, #14315872, … |
| maximal quotient of | C5×#72078, C5×#70652, C5×#70649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4887);