Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D65⋊D121 |
| unambiguous semidirect product | D605⋊D13 |
| unambiguous semidirect product | D1573⋊D5 |
| Fitting, derived, Hall | C5×C13×C121 ⋊ C22 |
| Hall | C13×C121 ⋊ C2×D5 |
| Hall | C5×C121 ⋊ C2×D13 |
| Sylow | C121 ⋊ D5×D13 |
| Hall | C5×C13 ⋊ C2×D121 |
| Sylow | C13 ⋊ D5×D121 |
| Sylow | C5 ⋊ D13×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C13×C121 | C22 |
| Frattini | C11 | D55⋊D13 |
| socle | C5×C11×C13 | C2×D11 |
| LCS | G ▷ C5×C13×C121 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
Polycyclic presentation:
2^2,5,11,13,11|d^11=f^10,d^a=d^10f,e^a=e^12,f^a=f^10,c^b=c^4,d^b=d^10f,f^b=f^102072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 39);