Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #88372⋊C3 |
| Sylow | C27⋊C3 ⋊ C22⋊C4 |
168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2^2,3^3|a^2=e,f^3=g,g^3=h,b^a=bd,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,f^c=fh150 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D27⋊C3, #72276234, #72276267 |
| maximal normal subgroup of | C22⋊C4×D27⋊C3, #72276234, #72276267 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 439);