Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C9×#416 ⋊ C2 |
| Sylow | C9 ⋊ #2897 |
1167 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=f,e^2=g,h^3=i,b^a=be,e^a=eg,e^b=eg,d^c=dg,h^c=h^2i^2,i^c=i^2,h^d=h^2i^2,i^d=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92004);