Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#63447 |
| Fitting | C3×C9×C22⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ #124 |
262 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #13147935, #13147939, #13147941, … |
| maximal normal subgroup of | #13147935, #13147939, #13147941, … |
| maximal quotient of | C3×#10588326, C3×#10588330, C3×#10588353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1375);