Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65042 |
| Fitting | C3×C5×#101 ⋊ C2 |
| Hall | C3×C5 ⋊ #454 |
| Sylow | C5 ⋊ C3×#454 |
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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)(9,12,20,10,14,21,13,16)(11,17,22,24,19,23,18,15);(9,11,14,19)(10,15,16,24)(12,17,21,23)(13,22,20,18);(5,6)(7,8)(9,10)(11,15)(12,20)(13,21)(14,16)(17,18)(19,24)(22,23)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598575, #14279352, C3×#10599953, … |
| maximal normal subgroup of | C3×#10598575, #14279352, C3×#10599953, … |
| maximal quotient of | C3×#10598923, C3×#10598924, C3×#10598931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3845);