Finite Group DatabasebetaFinite Group Databasebeta| order | 20900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1045 |
| unambiguous semidirect product | C19⋊(C5×Dic55) |
| derived | C5×C11×C19 ⋊ C4×C5 |
| Hall | C52×C11×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ Dic11 |
| Hall | C52×C11 ⋊ Dic19 |
| Hall | C11×C19 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ Dic209 |
| Sylow | C19 ⋊ C5×Dic55 |
| Sylow | C11 ⋊ C5×Dic95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1045 |
| commutator, hypocenter | C5×C11×C19 | C4×C5 |
| Frattini | C2 | C5×D1045 |
| Fitting, socle, prime radical | C2×C52×C11×C19 | C2 |
| cosocle | C2×C5×C11×C19 | C2×C5 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C2×C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4180 |
5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20900, 50);