Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C9×#465 ⋊ C2 |
| Sylow | C9 ⋊ #3303 |
597 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=eg,b^2=g,d^2=g,f^2=g,h^3=i,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^c=h^2i^2,i^c=i^2,h^d=h^2i^2,i^d=i^2123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 122113);