Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | #261×C121⋊C5 |
| unambiguous semidirect product | (#261×C121)⋊C5 |
| Fitting, derived, Hall | C13×C121 ⋊ C4×C5 |
| Hall | C13×C121⋊C5 ⋊ C4 |
| Hall | #261×C121 ⋊ C5 |
| Sylow | C121 ⋊ C5×#261 |
| Sylow | C13 ⋊ C4×C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C121 | C4×C5 |
| Frattini | C11 | #261×C11⋊C5 |
| socle | C11×C13 | C4×C11⋊C5 |
| prime radical | D13×C121⋊C5 | C2 |
| cosocle | D13×C121 | C2×C5 |
| LCS | G ▷ C13×C121 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 16);