Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D475 |
| unambiguous semidirect product | C19⋊(C17×D25) |
| unambiguous semidirect product | C25⋊(C17×D19) |
| Fitting, Hall | C17×C19×C25 ⋊ C2 |
| derived, Hall | C19×C25 ⋊ C2×C17 |
| Hall | C17×C25 ⋊ D19 |
| Hall | C17×C19 ⋊ D25 |
| Sylow | C25 ⋊ C17×D19 |
| Sylow | C19 ⋊ C17×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D475 |
| commutator, cosocle, hypocenter | C19×C25 | C2×C17 |
| Frattini | C5 | C17×D95 |
| Fitting | C17×C19×C25 | C2 |
| socle | C5×C17×C19 | D5 |
| LCS | G ▷ C19×C25 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
4063 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D19×D25, D17×D475, D323⋊D25, … |
| maximal normal subgroup of | C17×D19×D25, D17×D475, D323⋊D25, … |
| maximal quotient of | C17×Dic475, C2×C17×D475 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 6);