Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×Dic9⋊C8 |
| unambiguous semidirect product | Dic9⋊(C5×C8) |
| Hall | C5×C9 ⋊ C4⋊C8 |
| Sylow | C9 ⋊ C5×C4⋊C8 |
114 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5)(6,11,13,12,7,9,8,14,10)(16,18)(19,20,21,23,22,24,25,26);(7,9)(8,12)(10,11)(13,14)(15,16,17,18)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 134);