Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C19 |
| direct product | C5×C3⋊(C19⋊Dic19) |
| unambiguous semidirect product | C3⋊(C5×C19⋊Dic19) |
| unambiguous semidirect product | C19⋊(C5×Dic57) |
| derived, Hall | C3×C192 ⋊ C4×C5 |
| Hall | C3×C5×C192 ⋊ C4 |
| Hall | C5×C192 ⋊ Dic3 |
| Sylow | C192 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ C19⋊Dic19 |
| Sylow | C3 ⋊ C5×C19⋊Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊(C19⋊D19) |
| commutator, hypocenter | C3×C192 | C4×C5 |
| Frattini | C2 | C5×C3⋊(C19⋊D19) |
| Fitting, socle, prime radical | C2×C3×C5×C192 | C2 |
| cosocle | C2×C3×C192 | C2×C5 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C2×C5 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21660 |
5430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 76);