Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#64996 |
| Fitting | C3×C5×#97 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×M16 |
| Sylow | C5 ⋊ C3×C4×M16 |
284 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 158 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)(4,5,7,8,6)(13,14,15,18,16,17,19,20);(9,10,11,12)(14,17)(18,20);(5,6)(7,8)(14,17)(18,20)240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598548, #14277229, C3×#10598543, … |
| maximal normal subgroup of | C3×#10598548, #14277229, C3×#10598543, … |
| maximal quotient of | C3×#10598860, C3×#10598863, C3×#10598865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3799);