Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | C22⋊#63540 |
| Sylow | C32 ⋊ C22⋊C32 |
180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=hi,i^a=hi^2,h^d=h^2,i^d=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6702);