Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#3664 |
| Fitting | C3×C8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×SD16 |
224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3664, D3×#63467, #13149755, … |
| maximal normal subgroup of | C2×D3×#3664, D3×#63467, #13149755, … |
| maximal quotient of | #13138138, #13138139, #13138140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 769);