Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C4 |
| direct product | C5×#4764 |
| Fitting | C3×C5×#102 ⋊ C2 |
| Hall | C3×C5 ⋊ #490 |
| Sylow | C3 ⋊ C5×#490 |
220 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 220 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,11,12,16)(10,14,13,15)(17,18)(19,24)(20,21)(22,23);(10,13)(14,15)(18,22)(19,23)(21,24);(7,8)(9,10,12,13)(11,15,16,14)(18,21)(22,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#490, C2×C5×#4764, D5×#4764, … |
| maximal normal subgroup of | C5×D3×#490, C2×C5×#4764, D5×#4764, … |
| maximal quotient of | C5×#68849, C5×#70188, C5×#68856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4458);