Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D8×D9 |
| Fitting | C3×C9×D8 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×D8 |
250 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#826, #13139227, D9×#827, … |
| maximal normal subgroup of | D9×#826, #13139227, D9×#827, … |
| maximal quotient of | C3×#10588439, C3×#10588466, C3×#10588440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1496);