Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #103 |
210 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=cd,c^2=e,f^3=h,b^a=bc,c^a=ce,f^a=f^2h^2,g^a=g^2,h^a=h^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #13138132, #13138136, #13138139, … |
| maximal normal subgroup of | #13138132, #13138136, #13138139, … |
| maximal quotient of | #13135743, #13135763, #13135789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 506);