Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32×C4 |
| direct product | C3×C9⋊(C42⋊C3) |
| Fitting | C3×C42×C9 ⋊ C3 |
| Sylow | C42 ⋊ C3×3−1+2 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1498);