Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#65120 |
| Hall | C3×C5 ⋊ #446 |
| Sylow | C5 ⋊ C3×#446 |
188 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 106 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)(4,5,7,8,6)(11,15)(13,16)(17,19,20,22,21,23,24,18);(9,11,12,15)(10,13,14,16);(5,6)(7,8)(9,10,12,14)(11,13,15,16)(17,18,20,19,21,22,24,23)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598582, #14277968, C3×#10598947, … |
| maximal normal subgroup of | C3×#10598582, #14277968, C3×#10598947, … |
| maximal quotient of | C3×#10601259, C3×#10599446, C3×#10599448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3923);