Finite Group DatabasebetaFinite Group Databasebeta| order | 9909 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C367⋊C27 |
| derived, Sylow | C367 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C367⋊C3 |
| commutator, hypocenter | C367 | C27 |
| Fitting, cosocle | C9×C367 | C3 |
| socle, prime radical | C3×C367 | C9 |
| LCS | G ▷ C367 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,367|a^3=b,b^3=c,d^a=d^2831125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C27×C367⋊C3, C3×C367⋊C27, #44446204, … |
| maximal normal subgroup of | C27×C367⋊C3, C3×C367⋊C27, #44446204, … |
| maximal quotient of | C367⋊C81, C3×C367⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9909, 6);