Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C4 |
| unambiguous semidirect product | C4⋊(#127⋊C9) |
| unambiguous semidirect product | #2867⋊C9 |
| Sylow | #2867 ⋊ C9 |
480 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 480 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) = 36 |
Polycyclic presentation:
2^2,3,2,3,2^4|b^2=d,c^3=e,f^2=h,g^2=i,b^a=bd,f^a=fh,g^a=gi,c^b=ch,f^c=fg,g^c=fi,h^c=hi,i^c=h84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153524);