Finite Group DatabasebetaFinite Group Databasebeta| order | 13794 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D11×C19⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C11×C19⋊C3) |
| unambiguous semidirect product | (C19×D11)⋊(C3×C11) |
| unambiguous semidirect product | (C11×C19×D11)⋊C3 |
| Fitting, socle, Hall | C112×C19 ⋊ C2×C3 |
| derived | C11×C19 ⋊ C2×C3×C11 |
| Hall | C112×C19⋊C3 ⋊ C2 |
| Hall | C11×C19×D11 ⋊ C3 |
| Sylow | C112 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ C3×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D11×C19⋊C3 |
| commutator, cosocle, hypocenter | C11×C19 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C19 | C2×C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
693 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D19⋊C3, D11×C11⋊(D19⋊C3), D112×C19⋊C3, … |
| maximal normal subgroup of | C11×D11×D19⋊C3, D11×C11⋊(D19⋊C3), D112×C19⋊C3, … |
| maximal quotient of | C11×Dic11×C19⋊C3, C2×C11×D11×C19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13794, 16);