Finite Group DatabasebetaFinite Group Databasebeta| order | 15860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15691760⋊C5 |
| Fitting, socle, derived, Hall | C13×C61 ⋊ C4×C5 |
| Hall | C13×C61⋊C5 ⋊ C4 |
| Hall | #15691760 ⋊ C5 |
| Hall | C61⋊C5 ⋊ #261 |
| Sylow | C61 ⋊ C5×#261 |
| Sylow | C13 ⋊ Dic61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C61 | C4×C5 |
| prime radical | D13×C61⋊C5 | C2 |
| cosocle | D13×C61 | C2×C5 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 793 |
Polycyclic presentation:
2,5,2,13,61|a^2=c,d^a=d^5,e^a=e^60,e^b=e^9,d^c=d^1283 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15860, 17);