Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊(C11⋊#261) |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C4×C5 |
| Hall | C11×C13×C11⋊C5 ⋊ C4 |
| Hall | C11⋊(C11⋊#261) ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ #261 |
| Sylow | C112 ⋊ C5×#261 |
| Sylow | C13 ⋊ (C11⋊C5)⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C4×C5 |
| prime radical | C11×D13×C11⋊C5 | C2 |
| cosocle | C112×D13 | C2×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 715 |
Polycyclic presentation:
2,5,2,11^2,13|a^2=c,d^a=d^10,e^a=e^10,f^a=f^5,d^b=d^4,f^c=f^12323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 104);