Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C81 · Schur multiplier (H2) = C9 |
| direct product | C81×#4296 |
| Fitting | C19×C81 ⋊ C9 |
| derived, Sylow | C19 ⋊ C9×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C81 | #4296 |
| commutator, hypocenter | C19 | C9×C81 |
| Frattini | C27 | C3×#4296 |
| Fitting | C19×C81 | C9 |
| socle | C3×C19 | C9×C27 |
| prime radical | C3×C19⋊C3 | C3×C27 |
| cosocle | C27×C19⋊C3 | C32 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C81 | |
98 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, 4112);