Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
No aliases for this group.
| Fitting | C2×C32×#135 ⋊ C2 |
| Sylow | C32 ⋊ #3584 |
4272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^d=h^2,i^d=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152968);