Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4559 |
| Hall | C3×C5 ⋊ #344 |
| Sylow | C3 ⋊ C5×#344 |
180 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 94 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)(9,11,13,20,14,21,12,19)(10,15,16,23,17,18,22,24);(7,8)(9,10,12,16,14,17,13,22)(11,18,19,24,21,15,20,23)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#344, C2×C5×#4559, D5×#4559, … |
| maximal normal subgroup of | C5×D3×#344, C2×C5×#4559, D5×#4559, … |
| maximal quotient of | C5×#67741, C5×#67678, C5×#67668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 453);