Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #2032⋊C9 |
| derived | #543 ⋊ C2×C9 |
| Sylow | #2032 ⋊ C9 |
144 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 22 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:
2,3^2,2^6|b^3=c,d^2=h,e^2=h,d^a=df,e^a=eg,h^a=hi,d^b=de,e^b=d,f^b=fgi,g^b=f,e^d=eh,f^d=fi,f^e=fi,g^e=gi63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153378);