Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C9×C22⋊C8 ⋊ C2 |
| Sylow | C9 ⋊ #1459 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=g,e^2=g,h^3=i,b^a=bd,d^a=df,e^b=ef,h^b=h^2i^2,i^b=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7788);