Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C27 · Schur multiplier (H2) = C32×C9 |
| direct product | C3×C27×#4296 |
| Fitting | C3×C19×C27 ⋊ C9 |
| derived, Sylow | C19 ⋊ C3×C9×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | #4296 |
| commutator, hypocenter | C19 | C3×C9×C27 |
| Frattini | C9 | C32×#4296 |
| Fitting | C3×C19×C27 | C9 |
| socle | C32×C19 | C92 |
| prime radical | C32×C19⋊C3 | C3×C9 |
| cosocle | C9×C19⋊C3 | C33 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C27 | |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4233);