Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#65785 |
| Fitting | C2×C3×C5×Q8 ⋊ C4 |
| Hall | C3×C5 ⋊ #410 |
| Sylow | C5 ⋊ C3×#410 |
316 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 96 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)(9,12,13,21)(10,15,16,19)(11,17,18,20)(14,22,23,24);(9,11,13,18)(10,14,16,23)(12,20,21,17)(15,24,19,22);(5,6,7,8)(9,10)(11,14)(12,19,21,15)(13,16)(17,24,20,22)(18,23)96 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598578, #14279178, C3×#10603932, … |
| maximal normal subgroup of | C3×#10598578, #14279178, C3×#10603932, … |
| maximal quotient of | C3×#10604289, C3×#10604290, C3×#10604976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6513);