Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×C4×D4 ⋊ C22 |
| Sylow | C32 ⋊ #3428 |
3249 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^2,i^d=i^2,i^e=hi^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134138);