Finite Group DatabasebetaFinite Group Databasebeta| order | 31450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D3145 |
| unambiguous semidirect product | C17⋊(C5⋊D185) |
| unambiguous semidirect product | C37⋊(C5⋊D85) |
| Fitting, socle, derived, Hall | C52×C17×C37 ⋊ C2 |
| Hall | C52×C37 ⋊ D17 |
| Hall | C17×C37 ⋊ C5⋊D5 |
| Hall | C52×C17 ⋊ D37 |
| Sylow | C37 ⋊ C5⋊D85 |
| Sylow | C52 ⋊ D629 |
| Sylow | C17 ⋊ C5⋊D185 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C17×C37 | C2 |
| LCS | G ▷ C52×C17×C37 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15725 |
Polycyclic presentation:
2,5^2,17,37|b^a=b^4,c^a=c^4,d^a=d^16,e^a=e^367864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31450, 20);