Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C121⋊C5)⋊#261 |
| unambiguous semidirect product | (C121⋊#261)⋊C5 |
| Fitting, derived, Hall | C13×C121 ⋊ C4×C5 |
| Hall | C13×C121⋊C5 ⋊ C4 |
| Hall | C121⋊#261 ⋊ C5 |
| Hall | C121⋊C5 ⋊ #261 |
| Sylow | C121 ⋊ C5×#261 |
| Sylow | C13 ⋊ Dic121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C121 | C4×C5 |
| Frattini | C11 | (C11⋊C5)⋊#261 |
| socle | C11×C13 | Dic11⋊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 |
Polycyclic presentation:
2,5,2,11,13,11|a^2=c,d^11=f^10,d^a=d^10f,e^a=e^5,f^a=f^10,d^b=d^4f^4,f^b=f^4,e^c=e^12131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 14);