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×(C22⋊C9)⋊C9 |
| Sylow | C24 ⋊ C9⋊C9 |
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #72229281, #72229373, C22×#11757845, … |
| maximal normal subgroup of | #72229281, #72229373, C22×#11757845, … |
| maximal quotient of | C22×#11757417, C22×#13048081, C22×(C22⋊C9)⋊(C22⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1868);