Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×M16 |
226 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 65 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=ce,g^a=g^2,c^b=ce,f^b=f^2h^2,h^b=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720801, #13149745, #13149746, … |
| maximal normal subgroup of | C2×#11720801, #13149745, #13149746, … |
| maximal quotient of | #13138123, #13138124, #13138125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 768);