Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #2275⋊C9 |
| Sylow | #2275 ⋊ C9 |
309 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 309 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) = 72 |
Polycyclic presentation:
2^2,3^2,2^5|c^3=d,e^2=g,f^2=hi,b^a=bgh,c^a=ch,c^b=cgi,e^c=fh,f^c=efgh,g^c=hi,h^c=gi,i^c=g,f^e=fgh108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153412);