Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ AGL(1,ℤ/8) |
224 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|c^2=d,d^2=e,f^3=h,c^a=cd,d^a=de,g^a=g^2,c^b=cde,d^b=de,f^b=f^2h^2,h^b=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720820, #13149781, #13149783, … |
| maximal normal subgroup of | C2×#11720820, #13149781, #13149783, … |
| maximal quotient of | #13138267, #13138269, #13138271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 787);