Finite Group DatabasebetaFinite Group Databasebeta| order | 9218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D419⋊C11 |
| unambiguous semidirect product | (C419⋊C11)⋊C2 |
| Fitting, socle, derived, Sylow | C419 ⋊ C2×C11 |
| Hall | C419⋊C11 ⋊ C2 |
| Hall | D419 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C419 | C2×C11 |
| LCS | G ▷ C419 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,419|c^a=c^418,c^b=c^33441 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D419⋊C11, C3×D419⋊C11, C3⋊(D419⋊C11) |
| maximal normal subgroup of | C2×D419⋊C11, C3×D419⋊C11 |
| maximal quotient of | Dic419⋊C11, C2×D419⋊C11, C3×D419⋊C11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9218, 1);