Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C22 |
| direct product | C22×#66353 |
| Sylow | C24 ⋊ C27⋊C3 |
310 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #72229223, C22×#11757417, #72229244, … |
| maximal normal subgroup of | #72229223, C22×#11757417, #72229244, … |
| maximal quotient of | C23×#66353, #72275938 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1866);