Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D121 |
| unambiguous semidirect product | C121⋊(C2×C67) |
| Fitting, Hall | C67×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C2×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D121 |
| commutator, cosocle, hypocenter | C121 | C2×C67 |
| Frattini | C11 | D11×C67 |
| Fitting | C67×C121 | C2 |
| socle | C11×C67 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C67 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8107 |
4154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D67×D121, C2×C67×D121 |
| maximal normal subgroup of | D67×D121, C2×C67×D121 |
| maximal quotient of | C67×Dic121, C2×C67×D121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16214, 4);