Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#63460 |
| Fitting | C3×C9×C4⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ #126 |
206 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #13148864, #13148865, #13148868, … |
| maximal normal subgroup of | #13148864, #13148865, #13148868, … |
| maximal quotient of | C3×#10588331, C3×#10588340, C3×C9⋊#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1419);