Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D9)⋊C32 |
| Fitting | C2×C9×C32 ⋊ C2 |
| Sylow | C9 ⋊ C22⋊C32 |
123 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=d,d^2=e,e^2=f,f^2=g,h^3=i,b^a=bc,h^b=h^2i^2,i^b=i^2336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6696);