Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #87502⋊C3 |
211 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^2,3,2,3,2^4|a^2=d,b^2=d,b^a=bd,e^a=e^2,f^a=h,g^a=i,h^a=f,i^a=g,f^c=g,g^c=fg,h^c=i,i^c=hi,f^e=g,g^e=fg,h^e=hi,i^e=h44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157507);