Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C82 · Schur multiplier (H2) = C8 |
| direct product | C8×3−1+2⋊C8 |
| unambiguous semidirect product | 3−1+2⋊C82 |
| unambiguous semidirect product | (C8×C9⋊C8)⋊C3 |
| derived | C9 ⋊ C3×C82 |
| Sylow | 3−1+2 ⋊ C82 |
244 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C82×AGL(1,ℤ/9), #72245269, #72252883, … |
| maximal normal subgroup of | C82×AGL(1,ℤ/9), #72245269, #72252883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 1356);