Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C2×C4 |
| direct product | C9×#926 |
| Sylow | C3×C9 ⋊ #117 |
282 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 147 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 | #13135126, #13135127, #13135128, … |
| maximal normal subgroup of | #13135126, #13135127, #13135128, … |
| maximal quotient of | C9×#4925, C9×#4926, C9×#4932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1549);