Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ C4⋊C8 |
190 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 97 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=c,c^2=e,f^3=h,b^a=bd,f^a=f^2h^2,g^a=g^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13138112, #13138113, #13138117, … |
| maximal normal subgroup of | #13138112, #13138113, #13138117, … |
| maximal quotient of | #13135786, #13135787, #13135827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 504);