Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4485 |
| Fitting | C3×C5×C4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #331 |
| Sylow | C3 ⋊ C5×#331 |
168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,10,11,14,12,13,15,16)(18,21)(19,24)(22,23);(7,8)(10,13)(11,15)(17,18)(19,21)(20,23)(22,24)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#331, C2×C5×#4485, D5×#4485, … |
| maximal normal subgroup of | C5×D3×#331, C2×C5×#4485, D5×#4485, … |
| maximal quotient of | C5×#67479, C5×#67702, C5×#67571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 379);