Finite Group DatabasebetaFinite Group Databasebeta| order | 21850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D437 |
| unambiguous semidirect product | C19⋊(C52×D23) |
| unambiguous semidirect product | C23⋊(C52×D19) |
| Fitting, socle, Hall | C52×C19×C23 ⋊ C2 |
| derived, Hall | C19×C23 ⋊ C2×C52 |
| Hall | C52×C23 ⋊ D19 |
| Hall | C52×C19 ⋊ D23 |
| Sylow | C23 ⋊ C52×D19 |
| Sylow | C19 ⋊ C52×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D437 |
| commutator, cosocle, hypocenter | C19×C23 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C19×C23 | C2 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10925 |
5500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21850, 12);