Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #3028⋊C9 |
| Sylow | #3028 ⋊ C9 |
290 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 31 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:
2^2,3^2,2^5|a^2=i,b^2=i,c^3=d,e^2=i,f^2=i,b^a=bi,e^a=eg,f^a=fh,e^c=ef,f^c=e,g^c=ghi,h^c=g,f^e=fi,h^e=hi,g^f=gi69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153606);