Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D67⋊C121 |
| unambiguous semidirect product | (C67⋊C121)⋊C2 |
| derived, Sylow | C67 ⋊ C2×C121 |
| Hall | C67⋊C121 ⋊ C2 |
| Hall | D67 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | D67⋊C11 |
| commutator, hypocenter | C67 | C2×C121 |
| Fitting, socle, cosocle | C11×C67 | C2×C11 |
| prime radical | C11×D67 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8107 |
Polycyclic presentation:
2,11,67,11|b^11=d,c^a=c^66,c^b=c^64275 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D67⋊C121 |
| maximal normal subgroup of | C2×D67⋊C121 |
| maximal quotient of | Dic67⋊C121, C2×D67⋊C121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16214, 2);