Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×C9 ⋊ C22⋊Q8 |
260 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 67 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|b^2=d,c^2=d,f^3=h,c^a=cde,g^a=g^2,c^b=ce,f^b=f^2h^2,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #13147512, #13147526, #13147565, … |
| maximal normal subgroup of | #13147512, #13147526, #13147565, … |
| maximal quotient of | #13137729, #13137730, #13137731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 991);