Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C22 |
| direct product | C5×(C2×D3)⋊C16 |
| unambiguous semidirect product | (C2×D3)⋊(C5×C16) |
| Fitting | C2×C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ C22⋊C16 |
| Sylow | C3 ⋊ C5×C22⋊C16 |
132 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,14,15,18,16,19,21,24,17,20,22,25,23,26,27,28);(7,8)(9,10)(11,12)360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 401);