Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#64983 |
| Fitting | C3×C4×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #486 |
| Sylow | C5 ⋊ C3×#486 |
236 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 236 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,14)(13,15)(17,18,19,21,20,22,23,24);(9,11,12,16)(10,13,14,15);(5,6)(7,8)(9,10)(11,15)(12,14)(13,16)(18,21)(19,23)(22,24)258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598993, C3×#10598973, #14289126, … |
| maximal normal subgroup of | C3×#10598993, C3×#10598973, #14289126, … |
| maximal quotient of | C3×#10600555, C3×#10600561, C3×#10600565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3786);