Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4518 |
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ #360 |
| Sylow | C3 ⋊ C5×#360 |
116 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,11,19,10,14,21,12,16,15,22,18,17,13,24,23,20);(7,8)(9,10)(11,18)(12,21)(13,16)(14,20)(15,17)(19,22)(23,24)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#360, C2×C5×#4518, D5×#4518, … |
| maximal normal subgroup of | C5×D3×#360, C2×C5×#4518, D5×#4518, … |
| maximal quotient of | C5×#67516, C5×#67517, C5×#67526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 412);