Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #3584⋊C9 |
| Sylow | #3584 ⋊ C9 |
610 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^3,3,2,3,2^3|a^2=i,b^2=i,c^2=i,d^3=f,e^2=i,g^2=i,h^2=i,b^a=be,e^a=ei,e^b=ei,g^d=gh,h^d=g,h^g=hi156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153816);