Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C17 · Schur multiplier (H2) = C5 |
| direct product | C52×C17×D19 |
| unambiguous semidirect product | C19⋊(C2×C52×C17) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C52×C17 |
| Hall | C52×C19 ⋊ C2×C17 |
| Hall | C17×C19 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C17 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C52×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C52×C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
4675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D17×D19, C5×D5×C17×D19, C5×D19×D85, … |
| maximal normal subgroup of | C52×D17×D19, C5×D5×C17×D19, C5×D19×D85, … |
| maximal quotient of | C52×C17×Dic19, C2×C52×C17×D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 20);