Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(#131⋊C9) |
| unambiguous semidirect product | #2906⋊C9 |
| Sylow | #2906 ⋊ C9 |
236 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^2,3,2^2,3,2^3|a^2=e,b^2=d,c^3=f,e^2=i,g^2=i,h^2=i,b^a=bd,g^c=gh,h^c=g,h^g=hi210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153566);