Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | D3×C9×Q16 |
| Fitting | C3×C9×Q16 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×Q16 |
198 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63387, #13139255, #13139257, … |
| maximal normal subgroup of | D3×#63387, #13139255, #13139257, … |
| maximal quotient of | C9×#4792, C9×#4793, C9×#4795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1527);