Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C9×#496 ⋊ C2 |
| Sylow | C9 ⋊ #3264 |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|e^2=g,h^3=i,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^b=h^2i^2,i^b=i^2,h^c=h^2i^2,i^c=i^2,e^d=eg,h^d=h^2i^2,i^d=i^293 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 117764);