Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D81 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic81 |
| unambiguous semidirect product | C81⋊C42 |
| derived, Sylow | C81 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D81 |
| commutator, hypocenter | C81 | C42 |
| Frattini | C22×C27 | C2×D3 |
| Fitting | C2×C4×C81 | C2 |
| socle, prime radical | C22×C3 | C2×D27 |
| cosocle | C22×C81 | C22 |
| LCS | G ▷ C81 | |
| UCS | C1 ◁ C2×C4 | |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 11);