Finite Group DatabasebetaFinite Group Databasebeta| order | 21850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D2185 |
| unambiguous semidirect product | C19⋊(C5⋊D115) |
| unambiguous semidirect product | C23⋊(C5⋊D95) |
| Fitting, socle, derived, Hall | C52×C19×C23 ⋊ C2 |
| Hall | C52×C23 ⋊ D19 |
| Hall | C52×C19 ⋊ D23 |
| Hall | C19×C23 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D437 |
| Sylow | C23 ⋊ C5⋊D95 |
| Sylow | C19 ⋊ C5⋊D115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C19×C23 | C2 |
| LCS | G ▷ C52×C19×C23 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10925 |
Polycyclic presentation:
2,5^2,19,23|b^a=b^4,c^a=c^4,d^a=d^18,e^a=e^225464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21850, 20);