Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×#215 |
| unambiguous semidirect product | (C32×#215)⋊C3 |
| Fitting | C3×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ SD16 |
322 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1591);