Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22 |
| direct product | C3×#64753 |
| Hall | C3×C5 ⋊ #344 |
| Sylow | C5 ⋊ C3×#344 |
180 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 94 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)(4,5,7,8,6)(9,11)(10,14,16,17)(12,18)(13,19)(15,22,23,24)(20,21);(5,6)(7,8)(9,10,12,15,13,16,20,23)(11,17,18,24,19,14,21,22)186 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#344, C2×C3×#64753, #14294829, … |
| maximal normal subgroup of | C3×D5×#344, C2×C3×#64753, #14294829, … |
| maximal quotient of | C3×#10598232, C3×#10598108, C3×#10598235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 305);