Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊(#126⋊C9) |
| unambiguous semidirect product | #2860⋊C9 |
| Sylow | #2860 ⋊ C9 |
228 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3,2^4|b^2=d,c^3=e,f^2=i,g^2=h,b^a=bd,c^a=ci,f^a=fhi,g^a=gi,f^c=fg,g^c=fh,h^c=i,i^c=hi84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153520);