Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #1383 |
204 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,c^2=f,e^2=f,f^2=g,h^3=i,b^a=bc,c^a=cf,e^a=ef,f^a=fg,d^b=dg,h^b=h^2i^2,i^b=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6425);