Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #123 |
268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=d,f^3=h,b^a=bd,g^a=g^2,c^b=ce,f^b=f^2h^2,h^b=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #13147610, #13147613, #13147615, … |
| maximal normal subgroup of | #13147610, #13147613, #13147615, … |
| maximal quotient of | #13137672, #13137676, #13137680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 921);