Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #3522⋊C9 |
| Sylow | #3522 ⋊ C9 |
501 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 501 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^3,3,2,3,2^3|a^2=i,c^2=ei,d^3=f,g^2=i,h^2=i,b^a=be,c^a=ci,g^d=h,h^d=ghi,h^g=hi156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153776);