Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×C9 ⋊ C4⋊Q8 |
242 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=d,c^2=e,g^3=h,b^a=bd,c^a=ce,g^a=g^2h^2,h^a=h^2,f^b=f^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #13137493, #13137494, #13137495, … |
| maximal normal subgroup of | #13137493, #13137494, #13137495, … |
| maximal quotient of | #13137087, #13137090, #13137091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 899);