Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#949 |
| Fitting | C3×C9×#41 ⋊ C2 |
| Sylow | C3×C9 ⋊ AGL(1,ℤ/8) |
244 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 244 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) = 144 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #13141031, #13141032, #13141033, … |
| maximal normal subgroup of | #13141031, #13141032, #13141033, … |
| maximal quotient of | C9×#4995, C9×#5001, C9×#5003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1653);