Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C3×Q8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22⋊Q8 |
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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|b^2=e,c^2=e,f^3=h,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 | #13140714, #13140716, #13140720, … |
| maximal normal subgroup of | #13140714, #13140716, #13140720, … |
| maximal quotient of | #13144323, #13144324, #13144327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1823);