Finite Group DatabasebetaFinite Group Databasebeta| order | 23850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3975 |
| unambiguous semidirect product | C25⋊(C3⋊D159) |
| unambiguous semidirect product | C53⋊(C3⋊D75) |
| Fitting, derived, Hall | C32×C25×C53 ⋊ C2 |
| Hall | C25×C53 ⋊ C3⋊D3 |
| Hall | C32×C53 ⋊ D25 |
| Hall | C32×C25 ⋊ D53 |
| Sylow | C53 ⋊ C3⋊D75 |
| Sylow | C25 ⋊ C3⋊D159 |
| Sylow | C32 ⋊ D1325 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C25×C53 | C2 |
| Frattini | C5 | C3⋊D795 |
| socle | C32×C5×C53 | D5 |
| LCS | G ▷ C32×C25×C53 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11925 |
Polycyclic presentation:
2,3^2,5,53,5|d^5=f^4,b^a=b^2,c^a=c^2,d^a=d^4f,e^a=e^52,f^a=f^45964 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23850, 20);