Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65684 |
| Hall | C3×C5 ⋊ #432 |
| Sylow | C5 ⋊ C3×#432 |
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,8,7)(9,12,13,11)(10,14,15,16)(17,19,21,20)(18,23,22,24);(9,11,13,12)(10,14,15,16)(18,22)(23,24);(5,6,7,8)(9,10)(11,16)(12,14)(13,15)(17,18,20,23,21,22,19,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598544, #14276949, C3×#10598549, … |
| maximal normal subgroup of | C3×#10598544, #14276949, C3×#10598549, … |
| maximal quotient of | C3×#10604175, C3×#10604177, C3×#10604180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6412);