Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊(C3⋊#1084) |
| Sylow | C3×H(3,𝔽3) ⋊ C4⋊C4 |
638 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 243 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=c,b^a=bc,e^a=e^2,f^a=f^2,g^a=g^2,g^f=gh150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1735);