Finite Group DatabasebetaFinite Group Databasebeta| order | 19830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D661⋊C3)⋊C5 |
| unambiguous semidirect product | (D661⋊C5)⋊C3 |
| unambiguous semidirect product | ((C661⋊C3)⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C661 ⋊ C2×C3×C5 |
| Hall | (C661⋊C3)⋊C5 ⋊ C2 |
| Hall | D661⋊C5 ⋊ C3 |
| Hall | D661⋊C3 ⋊ C5 |
| Hall | C661⋊C5 ⋊ C2×C3 |
| Hall | C661⋊C3 ⋊ C2×C5 |
| Hall | D661 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C661 | C2×C3×C5 |
| LCS | G ▷ C661 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 661 |
Polycyclic presentation:
2,3,5,661|d^a=d^660,d^b=d^296,d^c=d^24752 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19830, 18);