Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#4827 |
| Fitting | C3×C5×#104 ⋊ C2 |
| Hall | C3×C5 ⋊ #454 |
| Sylow | C3 ⋊ C5×#454 |
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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 — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,12,23,11,14,20,13,21)(10,16,18,24,19,15,17,22);(9,11,14,21)(10,15,19,16)(12,23,20,13)(17,24,18,22);(7,8)(9,10)(11,15)(12,22)(13,18)(14,19)(16,21)(17,23)(20,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#454, C2×C5×#4827, D5×#4827, … |
| maximal normal subgroup of | C5×D3×#454, C2×C5×#4827, D5×#4827, … |
| maximal quotient of | C5×#68292, C5×#68324, C5×#68293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4521);