Finite Group DatabasebetaFinite Group Databasebeta| order | 19815 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C1321⋊C3)⋊C5 |
| unambiguous semidirect product | (C1321⋊C5)⋊C3 |
| Fitting, socle, derived, Sylow | C1321 ⋊ C3×C5 |
| Hall | C1321⋊C5 ⋊ C3 |
| Hall | C1321⋊C3 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1321 | C3×C5 |
| LCS | G ▷ C1321 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1321 |
Polycyclic presentation:
3,5,1321|c^a=c^297,c^b=c^133103 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19815, 1);