Finite Group DatabasebetaFinite Group Databasebeta| order | 13794 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2299 |
| unambiguous semidirect product | C121⋊(C3×D19) |
| Fitting, Hall | C3×C19×C121 ⋊ C2 |
| derived, Hall | C19×C121 ⋊ C2×C3 |
| Hall | C3×C121 ⋊ D19 |
| Sylow | C121 ⋊ C3×D19 |
| Hall | C3×C19 ⋊ D121 |
| Sylow | C19 ⋊ C3×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2299 |
| commutator, cosocle, hypocenter | C19×C121 | C2×C3 |
| Frattini | C11 | C3×D209 |
| Fitting | C3×C19×C121 | C2 |
| socle | C3×C11×C19 | D11 |
| LCS | G ▷ C19×C121 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6897 |
3453 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D121, D3×D2299, D57⋊D121, … |
| maximal normal subgroup of | C3×D19×D121, D3×D2299, D57⋊D121, … |
| maximal quotient of | C3×Dic2299, C2×C3×D2299 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13794, 8);