Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4875 |
| Hall | C3×C5 ⋊ #477 |
| Sylow | C3 ⋊ C5×#477 |
192 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(9,12,13,11)(10,14,15,16)(18,20)(19,23)(22,24);(9,11,13,12)(10,14,15,16)(17,19)(18,22)(20,23)(21,24);(7,8)(9,10,13,15)(11,14,12,16)(17,18,21,20)(19,22,24,23)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#477, C2×C5×#4875, D5×#4875, … |
| maximal normal subgroup of | C5×D3×#477, C2×C5×#4875, D5×#4875, … |
| maximal quotient of | C5×#68904, C5×#70642, C5×#68906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4569);