Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C27 · Schur multiplier (H2) = C36 |
| direct product | C32×(C19⋊C3)⋊C27 |
| unambiguous semidirect product | (C19⋊C3)⋊(C32×C27) |
| derived, Sylow | C19 ⋊ C33×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | #4296 |
| commutator, hypocenter | C19 | C33×C27 |
| Frattini | C3 | C33×#4296 |
| Fitting | C32×C9×C19 | C9 |
| socle | C33×C19 | C3×C9 |
| prime radical | C33×C19⋊C3 | C9 |
| cosocle | #4294 | C34 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C32×C9 | |
1160 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, 4416);