Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20262574⋊C5 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C4×C5 |
| Hall | C13×#10597243 ⋊ C4 |
| Hall | #20262574 ⋊ C5 |
| Hall | #10597243 ⋊ Dic13 |
| Sylow | C112 ⋊ C5×Dic13 |
| Sylow | C13 ⋊ #92150⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C4×C5 |
| prime radical | C13×#11925892 | C2 |
| cosocle | C13×C11⋊D11 | C2×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2,5,2,11^2,13|a^2=c,d^a=d^5e^7,e^a=de^6,f^a=f^12,d^b=d^3,e^b=e^3,d^c=d^10,e^c=e^10158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 97);