Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C4 |
| unambiguous semidirect product | C4⋊(C3⋊(#127⋊C3)) |
| unambiguous semidirect product | #73318⋊C3 |
| Fitting | C3×C43 ⋊ C2×C3 |
513 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 513 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) = 36 |
Polycyclic presentation:
2^2,3,2^3,3,2^2|b^2=d,e^2=h,f^2=hi,b^a=bd,e^a=eh,f^a=fhi,g^a=g^2,e^c=ef,f^c=ehi,h^c=i,i^c=hi60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155132);