Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | Q8×D27⋊C3 |
| unambiguous semidirect product | D27⋊(C3×Q8) |
| Fitting | Q8×C27⋊C3 ⋊ C2 |
| Sylow | C27⋊C3 ⋊ C2×Q8 |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1091);