Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | D3×C9×C4⋊C4 |
| Fitting | C3×C9×C4⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×C4⋊C4 |
302 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#63366, D3×#63367, #13137665, … |
| maximal normal subgroup of | D3×#63366, D3×#63367, #13137665, … |
| maximal quotient of | C9×#4667, C9×#4649, C9×#4650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1420);