Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | Q8×C3⋊D27 |
| Fitting | C3×Q8×C27 ⋊ C2 |
| Sylow | C3×C27 ⋊ C2×Q8 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1177);