Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×D67 |
| Fitting, Hall | C67×C121 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D67 |
| commutator, hypocenter | C67 | C2×C121 |
| Frattini | C11 | C11×D67 |
| Fitting | C67×C121 | C2 |
| socle, cosocle | C11×C67 | C2×C11 |
| prime radical | C11×D67 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C121 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8107 |
4235 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D67×D121, C2×C121×D67 |
| maximal normal subgroup of | D67×D121, C2×C121×D67 |
| maximal quotient of | C121×Dic67, C2×C121×D67 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16214, 5);