Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#901 |
| Fitting | C2×C3×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #131 |
208 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13135048, #13135049, C9×#4508, … |
| maximal normal subgroup of | #13135048, #13135049, C9×#4508, … |
| maximal quotient of | C8×C9×Dic6, C9×#4679, C8×C9×D12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1461);