Finite Group DatabasebetaFinite Group Databasebeta| order | 16226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1159 |
| unambiguous semidirect product | C19⋊(C7×D61) |
| unambiguous semidirect product | C61⋊(C7×D19) |
| Fitting, socle, Hall | C7×C19×C61 ⋊ C2 |
| derived, Hall | C19×C61 ⋊ C2×C7 |
| Hall | C7×C61 ⋊ D19 |
| Hall | C7×C19 ⋊ D61 |
| Sylow | C61 ⋊ C7×D19 |
| Sylow | C19 ⋊ C7×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1159 |
| commutator, cosocle, hypocenter | C19×C61 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C61 | C2 |
| LCS | G ▷ C19×C61 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8113 |
4067 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D61, D7×D1159, D133⋊D61, … |
| maximal normal subgroup of | C7×D19×D61, D7×D1159, D133⋊D61, … |
| maximal quotient of | C7×Dic1159, C2×C7×D1159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16226, 4);