Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C16 · Schur multiplier (H2) = C1 |
| direct product | C9×C9⋊C16 |
| derived | C9 ⋊ C9×C16 |
| Sylow | C92 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C9 | D9 |
| commutator, hypocenter | C9 | C9×C16 |
| Frattini | C32×C8 | C3×D3 |
| Fitting | C8×C92 | C2 |
| socle, prime radical | C2×C32 | C3×C3⋊C8 |
| cosocle | C3×C8×C9 | C2×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C8×C9 | |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 28);