Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×C9 ⋊ C4×Q8 |
236 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 79 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,f^3=h,c^a=cde,g^a=g^2,f^b=f^2h^2,h^b=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #13147461, #13147464, #13147468, … |
| maximal normal subgroup of | #13147461, #13147464, #13147468, … |
| maximal quotient of | #13138112, #13138117, #13138120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 868);