Finite Group DatabasebetaFinite Group Databasebeta| order | 35836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#11923876 |
| Fitting, Hall | C31×C289 ⋊ C4 |
| derived, Sylow | C289 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #11923876 |
| commutator, hypocenter | C289 | C4×C31 |
| Frattini | C17 | C31×#595 |
| Fitting | C31×C289 | C4 |
| socle | C17×C31 | #595 |
| prime radical | C31×D289 | C2 |
| cosocle | D289 | C2×C31 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C31 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8959 |
2356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35836, 6);