Finite Group DatabasebetaFinite Group Databasebeta| order | 15580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D95⋊D41 |
| unambiguous semidirect product | D205⋊D19 |
| unambiguous semidirect product | D779⋊D5 |
| Fitting, socle, derived, Hall | C5×C19×C41 ⋊ C22 |
| Hall | C19×C41 ⋊ C2×D5 |
| Hall | C5×C41 ⋊ C2×D19 |
| Hall | C5×C19 ⋊ C2×D41 |
| Sylow | C41 ⋊ D5×D19 |
| Sylow | C19 ⋊ D5×D41 |
| Sylow | C5 ⋊ D19×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C41 | C22 |
| LCS | G ▷ C5×C19×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3895 |
Polycyclic presentation:
2^2,5,19,41|d^a=d^18,e^a=e^40,c^b=c^4,d^b=d^181024 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15580, 39);