Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C9×M16 ⋊ C2 |
| Sylow | C9 ⋊ #1759 |
480 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 150 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=e,b^2=f,c^2=e,d^2=g,h^3=i,b^a=bd,d^a=dg,f^a=fg,h^a=h^2i^2,i^a=i^2,c^b=cg,h^b=h^2i^2,i^b=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17913);