Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32⋊C9 ⋊ C22⋊C4 |
251 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|b^2=c,f^3=g,b^a=bd,f^a=f^2g^2,g^a=g^2,h^a=h^2,e^b=e^2,h^b=h^2,f^e=fh78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 187);