Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C9 ⋊ #1882 |
501 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=df,d^2=g,e^2=g,f^2=g,h^3=i,b^a=bd,c^a=ce,e^a=eg,d^b=dg,f^b=fg,h^b=h^2i^2,i^b=i^2,e^c=eg144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 21673);