Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C3×H(3,𝔽3) ⋊ Q16 |
273 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 52 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=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,g^a=g^2,h^a=h^2,e^b=e^2,f^b=f^2,h^b=h^2,g^f=gh60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1401);