Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66440⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #66440⋊C4 |
| derived | C9×A4 ⋊ C3×C4 |
172 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2,3^3,2^2|a^2=c,e^3=f,d^a=d^2,e^a=e^2f^2,f^a=f^2,g^a=gh,d^b=df,e^b=ef^2,g^d=h,h^d=gh62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2119);