Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| direct product | D3×C9⋊SL(2,𝔽3) |
| unambiguous semidirect product | C3⋊(C2×C9⋊SL(2,𝔽3)) |
| unambiguous semidirect product | (D3×C9)⋊SL(2,𝔽3) |
| Fitting | C3×Q8×C9 ⋊ C2×C3 |
171 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2151);