Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×Q8×D9 |
| Fitting | C3×Q8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C22×Q8 |
506 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 506 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 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×SD16×D9, D9×#915, D3×#63477, … |
| maximal normal subgroup of | D3×SD16×D9, D9×#915, D3×#63477, … |
| maximal quotient of | #13148757, #13148758, #13148759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2478);