Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×D27 |
| Fitting | C3×Q8×C27 ⋊ C2 |
| Sylow | C3×C27 ⋊ C2×Q8 |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1087);