Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C81 · Schur multiplier (H2) = C33 |
| direct product | C3×(C19⋊C3)⋊C81 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×C81) |
| derived, Sylow | C19 ⋊ C32×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | #4296 |
| commutator, hypocenter | C19 | C32×C81 |
| Frattini | C9 | C32×#4296 |
| Fitting | C3×C19×C27 | C9 |
| socle | C32×C19 | C3×C27 |
| prime radical | C32×C19⋊C3 | C27 |
| cosocle | #10587018 | C33 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C27 | |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4617 |
891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4396);