Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C22×C3 |
| direct product | C22×C9⋊(C22⋊C9) |
| Sylow | C24 ⋊ C9⋊C9 |
360 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11757845, C22×(C22⋊C9)⋊(C22⋊C9) |
| maximal normal subgroup of | C22×#11757845 |
| maximal quotient of | C22×(C22⋊C9)⋊(C22⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1869);