Finite Group DatabasebetaFinite Group Databasebeta| order | 16214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C11×D67⋊C11 |
| unambiguous semidirect product | D67⋊C112 |
| unambiguous semidirect product | (C67⋊C11)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D67)⋊C11 |
| Fitting, socle | C11×C67 ⋊ C2×C11 |
| derived, Sylow | C67 ⋊ C2×C112 |
| Hall | C11×C67⋊C11 ⋊ C2 |
| Hall | D67 ⋊ C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D67⋊C11 |
| commutator, cosocle, hypocenter | C67 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C11×C67 | C2×C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 737 |
275 conjugacy classes. The character table is too large to display.
| 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, 8);