Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #83685⋊C3 |
247 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^2,3,2^4,3,2|a^2=d,b^2=ei,d^2=e,f^2=i,g^2=i,b^a=bde,h^a=h^2,d^b=de,f^c=fg,g^c=f,g^f=gi84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155319);