Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊(C9⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | C3⋊(C9⋊SL(2,ℤ/4)) |
| unambiguous semidirect product | C9⋊(C3⋊SL(2,ℤ/4)) |
| unambiguous semidirect product | A4⋊(C3⋊Dic9) |
| derived | C3×C9×A4 ⋊ C4 |
370 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^2,3^4,2^2|a^2=b,e^3=f,c^a=c^2,d^a=d^2,e^a=e^2f^2,f^a=f^2,g^a=gh,g^c=h,h^c=gh114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2136);