Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4516 |
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ #361 |
| Sylow | C3 ⋊ C5×#361 |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 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) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,10,11,18,19,21,24,22,13,15,20,14,12,16,17,23);(7,8)(10,14)(11,17)(12,19)(15,18)(16,23)(20,24)(21,22)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#361, C2×C5×#4516, D5×#4516, … |
| maximal normal subgroup of | C5×D3×#361, C2×C5×#4516, D5×#4516, … |
| maximal quotient of | C5×#67516, C5×#67527, C5×#67560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 410);