Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#66262 |
| Fitting | C2×C3×C5×Q8 ⋊ C4 |
| Hall | C3×C5 ⋊ #519 |
| Sylow | C5 ⋊ C3×#519 |
532 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 276 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 — 4 generators on 24 points:
(1,2,3)(4,5,6,8,7)(10,16)(14,22)(15,24)(21,23);(9,12,13,20)(10,15,16,24)(11,17,18,19)(14,21,22,23);(9,11,13,18)(10,14,16,22)(12,19,20,17)(15,23,24,21);(5,6,7,8)(9,10)(11,14)(12,15)(13,16)(17,21)(18,22)(19,23)(20,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603931, #14299653, C3×#10604670, … |
| maximal normal subgroup of | C3×#10603931, #14299653, C3×#10604670, … |
| maximal quotient of | C3×#10617098, C3×#10617208, C3×#10617527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11165);