Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C4 |
| direct product | C3×#65345 |
| Hall | C3×C5 ⋊ #488 |
| Sylow | C5 ⋊ C3×#488 |
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,7,8,6)(10,14)(11,15)(18,23)(19,26)(20,28)(22,29)(24,25)(30,31);(9,11,12,15)(10,13,14,16)(17,19)(18,22)(20,27)(21,26)(23,31)(24,29)(25,30)(28,32);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,20,24,21,25,28,23)(19,22,27,29,26,30,32,31)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598034, C3×#10598038, #14279547, … |
| maximal normal subgroup of | C3×#10598034, C3×#10598038, #14279547, … |
| maximal quotient of | C3×#10600340, C3×#10600467, C3×#10600437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4148);