Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#944 |
| Sylow | C3×C9 ⋊ C4⋊Q8 |
242 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | #13135212, C9×#4478, #13140652, … |
| maximal normal subgroup of | #13135212, C9×#4478, #13140652, … |
| maximal quotient of | C9×#4973, C9×#4975, C9×#4976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1628);