Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #85886⋊C3 |
781 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 781 conjugacy classes of subgroups — too many to draw. Only its 113 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:
2^3,3,2^3,3,2|a^2=i,b^2=i,c^2=e,f^2=i,g^2=i,b^a=bi,h^a=h^2,c^b=ci,f^d=fg,g^d=f,g^f=gi114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157229);