Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #3415⋊C9 |
| Sylow | #3415 ⋊ C9 |
177 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^2,3,2,3,2^4|a^2=i,b^2=i,c^3=e,d^2=fi,f^2=i,g^2=i,h^2=i,b^a=bd,d^a=df,f^a=fi,d^b=df,f^b=fi,g^c=gh,h^c=g,h^g=hi120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153642);