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×SD16 ⋊ C2 |
| Sylow | C3×C9 ⋊ #135 |
310 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 310 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) = 432 |
Polycyclic presentation:
2^5,3^3|c^2=e,d^2=e,f^3=h,b^a=be,c^a=ce,f^a=f^2h^2,g^a=g^2,h^a=h^2,c^b=cd,d^b=de,d^c=de105 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#916, D3×#63478, #13149937, … |
| maximal normal subgroup of | D9×#916, D3×#63478, #13149937, … |
| maximal quotient of | #13143901, #13143902, #13143907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1765);