Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C9×M16 ⋊ C2 |
| Sylow | C9 ⋊ #2873 |
846 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,e^2=g,h^3=i,d^a=dg,c^b=cg,h^c=h^2i^2,i^c=i^2228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91229);