Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#4803 |
| Fitting | C3×C5×#103 ⋊ C2 |
| Hall | C3×C5 ⋊ #417 |
| Sylow | C3 ⋊ C5×#417 |
324 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(14,18)(15,20)(17,19);(13,14,16,17)(15,18,20,19);(7,8)(14,17)(18,19)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#417, C2×C5×#4803, D5×#4803, … |
| maximal normal subgroup of | C5×D3×#417, C2×C5×#4803, D5×#4803, … |
| maximal quotient of | C5×#68230, C5×#68234, C5×#68238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4497);