Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #3458 |
2988 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^2,i^c=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135951);