Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#66260 |
| Hall | C3×C5 ⋊ #568 |
| Sylow | C5 ⋊ C3×#568 |
516 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 272 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 — 4 generators on 24 points:
(1,2,3)(4,5,6,8,7)(10,17)(15,23)(16,18)(22,24);(9,12,14,13)(10,16,17,18)(11,19,20,21)(15,22,23,24);(9,11,14,20)(10,15,17,23)(12,21,13,19)(16,24,18,22);(5,6,7,8)(9,10,13,18,14,17,12,16)(11,15,19,22,20,23,21,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603934, #14299706, C3×#10604569, … |
| maximal normal subgroup of | C3×#10603934, #14299706, C3×#10604569, … |
| maximal quotient of | C3×#10617074, C3×#10617184, C3×#10617516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11163);