Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊Dic27 |
| Sylow | C3×C27 ⋊ C22⋊C4 |
160 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^4,3^4|b^2=c,e^3=g,g^3=h,b^a=bd,f^a=f^2,e^b=e^2g^2h^2,g^b=g^2h^2,h^b=h^2174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 197);