Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#826 |
| Fitting | C3×C9×D8 ⋊ C2 |
| Sylow | C3×C9 ⋊ D16 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#826, #13139224, #13139225, … |
| maximal normal subgroup of | D9×#826, #13139224, #13139225, … |
| maximal quotient of | C9×#4489, C9×#4491, C9×#4519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 426);