Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #99 |
210 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=cd,f^3=h,b^a=bd,d^a=de,g^a=g^2,c^b=ce,d^b=de,f^b=f^2h^2,h^b=h^293 conjugacy classes — view the full character table.
| maximal subgroup of | #13137457, D9×#806, #13137460, … |
| maximal normal subgroup of | #13137457, D9×#806, #13137460, … |
| maximal quotient of | #13135107, #13135109, #13135111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 297);