Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#65449 |
| Fitting | C2×C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ #472 |
| Sylow | C5 ⋊ C3×#472 |
216 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 74 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)(4,5,7,8,6)(10,16)(11,19)(12,13)(15,22)(17,18)(20,21);(9,11,13,20,14,21,12,19)(10,15,17,23,18,22,16,24);(5,6)(7,8)(9,10)(11,15)(12,16)(13,17)(14,18)(19,24)(20,23)(21,22)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10602310, C3×#10602264, #14316397, … |
| maximal normal subgroup of | C3×#10602310, C3×#10602264, #14316397, … |
| maximal quotient of | C3×#10602075, C3×#10602079, C3×#10602165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4252);