Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #67⋊Dic9 |
| Sylow | C3×C9 ⋊ C4×D4 |
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 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) = 144 |
Polycyclic presentation:
2^5,3^3|b^2=d,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 | #13147929, #13147941, #13147950, … |
| maximal normal subgroup of | #13147929, #13147941, #13147950, … |
| maximal quotient of | #67⋊(C9⋊C8), #13139524, #13139528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1251);