Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C3×C8 |
No aliases for this group.
| Fitting | C32×C82 ⋊ C2 |
| Sylow | C32 ⋊ #1705 |
642 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|b^2=d,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2,i^a=i^2294 conjugacy classes — view the full character table.
| maximal subgroup of | #72214058, #72214093, C3⋊D3×#1705, … |
| maximal normal subgroup of | #72214058, #72214093, C3⋊D3×#1705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16429);