Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#64685 |
| Hall | C3×C5 ⋊ #330 |
| Sylow | C5 ⋊ C3×#330 |
120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,13,14,15)(17,19,20,18,22,23,21,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18,22,24)(19,20,23,21)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#330, C2×C3×#64685, #14283897, … |
| maximal normal subgroup of | C3×D5×#330, C2×C3×#64685, #14283897, … |
| maximal quotient of | C3×#10597968, C3×#10597969, C3×#10598150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 237);