Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊#157)) |
| Fitting | C34×C4 ⋊ C4 |
| Sylow | C34 ⋊ C4⋊C4 |
384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3^4|a^2=c,b^2=d,b^a=bd,e^a=ef,f^a=ef^2,g^a=g^2,h^a=h^2,e^c=e^2,f^c=f^2114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3311);