Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4452 |
| Hall | C3×C5 ⋊ #328 |
| Sylow | C3 ⋊ C5×#328 |
160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 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)(6,7,8)(9,11)(10,13,14,15)(12,16)(18,21,22,23);(7,8)(9,10,12,14)(11,15,16,13)(17,18)(19,21)(20,22)(23,24)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#328, C2×C5×#4452, D5×#4452, … |
| maximal normal subgroup of | C5×D3×#328, C2×C5×#4452, D5×#4452, … |
| maximal quotient of | C5×#67477, C5×#67480, C5×#67612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 346);