Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #84031⋊C3 |
457 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 457 conjugacy classes of subgroups — too many to draw. Only its 33 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:
2^2,3,2^5,3|a^2=d,b^2=d,b^a=bd,e^a=eg,f^a=fgh,i^a=i^2,e^c=ef,f^c=e,g^c=h,h^c=gh60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155365);