Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×3−1+2⋊C4 |
| derived | C9 ⋊ C22×C32×C4 |
| Sylow | C3×3−1+2 ⋊ C22×C4 |
646 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3×#1094⋊C4, #72245182 |
| maximal normal subgroup of | #72245182 |
| maximal quotient of | C22×C3×#1094⋊C4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2595);