Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C3×C9×C22⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ #120 |
650 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^5,3^3|c^2=d,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 | #13137467, #13143865, #13148003, … |
| maximal normal subgroup of | #13137467, #13143865, #13148003, … |
| maximal quotient of | #13143686, #13143687, #13143699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1695);