Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C27 · Schur multiplier (H2) = C22 |
| direct product | C27×#239 |
| Fitting | C3×Q8×C27 ⋊ C2 |
| Sylow | C3×C27 ⋊ #41 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1090);