Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4563 |
| Hall | C3×C5 ⋊ #361 |
| Sylow | C3 ⋊ C5×#361 |
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 54 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)(10,14)(11,19)(12,22)(15,16)(17,24)(18,21)(20,23);(7,8)(9,10,11,15,13,18,19,17)(12,21,20,16,23,14,22,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#361, C2×C5×#4563, D5×#4563, … |
| maximal normal subgroup of | C5×D3×#361, C2×C5×#4563, D5×#4563, … |
| maximal quotient of | C5×#67762, C5×#67775, C5×#67790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 457);