Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C9×#41 ⋊ C2 |
| Sylow | C9 ⋊ #1906 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=df,e^2=g,h^3=i,b^a=bd,c^a=ce,d^a=dg,h^a=h^2i^2,i^a=i^2,d^b=dg,e^b=eg,f^b=fg,d^c=dg,e^c=eg,f^c=fg192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 22572);