Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊((C19⋊Dic19)⋊C5) |
| unambiguous semidirect product | (C3⋊(C19⋊Dic19))⋊C5 |
| derived, Hall | C3×C192 ⋊ C4×C5 |
| Hall | C3×C192⋊C5 ⋊ C4 |
| Hall | C3⋊(C19⋊Dic19) ⋊ C5 |
| Hall | C192⋊C5 ⋊ Dic3 |
| Sylow | C192 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ (C19⋊Dic19)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊((C19⋊D19)⋊C5) |
| commutator, hypocenter | C3×C192 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C192 | C2×C5 |
| prime radical | C2×C3×C192⋊C5 | C2 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1140 |
Polycyclic presentation:
2,5,3,19^2,2|a^2=f,c^a=c^2,d^a=d^18,e^a=e^18,d^b=d^12e^8,e^b=d^14e^11246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 48);