Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C9×#519 ⋊ C2 |
| Sylow | C9 ⋊ C4×2−1+4 |
2238 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=f,c^2=f,e^2=g,h^3=i,b^a=bf,d^a=df,c^b=cf,h^e=h^2i^2,i^e=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134210);