Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C9⋊#1273 |
| Sylow | C9 ⋊ #1273 |
318 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,d^2=f,e^2=g,h^3=i,b^a=bc,h^b=h^2i^2,i^b=i^2336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4707);