Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊#63121 |
| Fitting, derived, Hall | C5×C13×C121 ⋊ C4 |
| Hall | C13×C121 ⋊ AGL(1,𝔽5) |
| Hall | C5×C121 ⋊ #261 |
| Sylow | C121 ⋊ #63121 |
| Hall | C5×C13 ⋊ Dic121 |
| Sylow | C13 ⋊ C121⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C121⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C13×C121 | C4 |
| Frattini | C11 | C11⋊#63121 |
| socle | C5×C11×C13 | Dic11 |
| prime radical | C11×D65 | D11 |
| cosocle | C121×D65 | C2 |
| LCS | G ▷ C5×C13×C121 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
Polycyclic presentation:
2^2,5,11,13,11|a^2=b,d^11=f^10,c^a=c^2,d^a=d^10f,e^a=e^8,f^a=f^10,c^b=c^4,e^b=e^122060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 30);