Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9 ⋊ #1355 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=f,d^2=e,e^2=g,h^3=i,b^a=bc,c^a=ce,f^a=fg,h^a=h^2i^2,i^a=i^2,c^b=cf,d^b=defg,e^b=eg,d^c=dg84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5997);