Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D67⋊C11) |
| unambiguous semidirect product | (C67⋊C11)⋊D11 |
| unambiguous semidirect product | D737⋊C11 |
| Fitting, socle, derived | C11×C67 ⋊ C2×C11 |
| Hall | C11×C67⋊C11 ⋊ C2 |
| Sylow | C67 ⋊ C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C67 | C2×C11 |
| LCS | G ▷ C11×C67 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 737 |
Polycyclic presentation:
2,11^2,67|c^a=c^10,d^a=d^66,d^b=d^64110 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D67⋊C11, C2×C11⋊(D67⋊C11) |
| maximal normal subgroup of | D11×D67⋊C11, C2×C11⋊(D67⋊C11) |
| maximal quotient of | C11⋊(Dic67⋊C11), C2×C11⋊(D67⋊C11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16214, 9);