Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C3×C9×C22⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ #123 |
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|c^2=de,f^3=h,b^a=be,c^a=cd,f^a=f^2h^2,g^a=g^2,h^a=h^2,c^b=ce144 conjugacy classes — view the full character table.
| maximal subgroup of | #13137466, #13143866, #13148017, … |
| maximal normal subgroup of | #13137466, #13143866, #13148017, … |
| maximal quotient of | #13143685, #13143692, #13143696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1699);