Finite Group DatabasebetaFinite Group Databasebeta| order | 14238 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D113⋊C7 |
| unambiguous semidirect product | D113⋊(C7×C9) |
| unambiguous semidirect product | (C113⋊C7)⋊(C2×C9) |
| unambiguous semidirect product | (C9×D113)⋊C7 |
| Fitting, Hall | C9×C113 ⋊ C2×C7 |
| derived, Sylow | C113 ⋊ C2×C7×C9 |
| Hall | C9×C113⋊C7 ⋊ C2 |
| Hall | C9×D113 ⋊ C7 |
| Hall | C113⋊C7 ⋊ C2×C9 |
| Hall | D113 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D113⋊C7 |
| commutator, hypocenter | C113 | C2×C7×C9 |
| Frattini | C3 | C3×D113⋊C7 |
| Fitting | C9×C113 | C2×C7 |
| socle, cosocle | C3×C113 | C2×C3×C7 |
| prime radical | C3×D113⋊C7 | C3 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1017 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#90673⋊C7, C9⋊(#90673⋊C7), D9×D113⋊C7, … |
| maximal normal subgroup of | C9×#90673⋊C7, C9⋊(#90673⋊C7), D9×D113⋊C7, … |
| maximal quotient of | C9×Dic113⋊C7, C2×C9×D113⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14238, 11);