Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65721 |
| Fitting | C2×C3×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #427 |
| Sylow | C5 ⋊ C3×#427 |
228 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 100 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)(4,5,6,8,7)(9,12,13,20,14,21,11,18)(10,16,15,19,17,23,22,24);(9,11,14,13)(10,15,17,22)(12,18,21,20)(16,19,23,24);(5,6,7,8)(9,10)(11,15)(12,19)(13,22)(14,17)(16,20)(18,23)(21,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598665, C3×#10598626, #14278871, … |
| maximal normal subgroup of | C3×#10598665, C3×#10598626, #14278871, … |
| maximal quotient of | C3×#10604694, C3×#10604695, C3×#10603814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6449);