Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×Q16 ⋊ Q8 |
| Sylow | C32 ⋊ #2227 |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=dg,b^2=d,c^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=hi,i^a=hi^2,h^b=i^2,i^b=h,e^c=ef,f^c=fg,h^d=h^2,i^d=i^236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 33616);