Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C9⋊#1308 |
| Sylow | C9 ⋊ #1308 |
183 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 76 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,b^2=e,d^2=fg,e^2=f,h^3=i,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^2i^2,i^b=i^2138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5278);