Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×D8×C3⋊D3 |
| Fitting | C33×D8 ⋊ C2 |
| Sylow | C33 ⋊ C2×D8 |
544 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590193, C3×#10590195, #13157210, … |
| maximal normal subgroup of | C3×#10590193, C3×#10590195, #13157210, … |
| maximal quotient of | C3×#10592458, C3×#10592485, C3×#10592459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3832);