Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C3×#65536 |
| Hall | C3×C5 ⋊ #379 |
| Sylow | C5 ⋊ C3×#379 |
1012 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(14,16);(18,20);(5,6)(7,8)(9,10,11,12)(13,14)(15,16)(17,18)(19,20)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598114, #14277357, C3×#10598837, … |
| maximal normal subgroup of | C3×#10598114, #14277357, C3×#10598837, … |
| maximal quotient of | C3×#10602920, C3×#10602924, C3×#10602927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4339);