Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ SD16 |
350 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 70 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|b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,h^a=h^2,d^b=de,g^c=gh96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1699);