Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C11⋊C5)⋊D11)⋊D13 |
| unambiguous semidirect product | (C13⋊AGL(1,𝔽11))⋊D11 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C22×C5 |
| Hall | C11×C13×C11⋊C5 ⋊ C22 |
| Hall | (C11⋊D11)⋊D13 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C2×D13 |
| Sylow | C112 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ D11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C22×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
Polycyclic presentation:
2^2,5,11^2,13|d^a=d^10,f^a=f^12,d^b=d^10,e^b=e^10,e^c=e^4353 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 109);