Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×(C27⋊C3)⋊C8 |
| unambiguous semidirect product | (C2×C27⋊C3)⋊C8 |
| unambiguous semidirect product | (C2×C27⋊C8)⋊C3 |
| derived | C27 ⋊ C2×C3×C8 |
| Sylow | C27⋊C3 ⋊ C2×C8 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 339);