Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64868 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64869 |
| Fitting | C3×C5×C4⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ #328 |
| Sylow | C5 ⋊ C3×#328 |
160 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 48 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 — 2 generators on 24 points:
(1,2,3)(4,5,6,8,7)(9,11,12,16)(10,13,14,15)(17,18,20,22)(19,24,23,21);(5,6,7,8)(9,10)(11,15,16,13)(12,14)(18,21)(19,23)(22,24)87 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#64869, C3×D5⋊#328, D3×#64869, … |
| maximal normal subgroup of | C2×C3×#64869, C3×D5⋊#328, D3×#64869, … |
| maximal quotient of | C3×#10598713, C3×#10598715, C3×#10598720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 841);