Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×Q8×C9 |
| Fitting | C2×C3×Q8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22×Q8 |
506 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 291 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×#63394, #13140774, #13140775, … |
| maximal normal subgroup of | D3×#63394, #13140774, #13140775, … |
| maximal quotient of | C2×C9×#887, C2×C9×#896, C2×C9×#888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2589);