Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×D85 |
| unambiguous semidirect product | C5⋊(C5×C19×D17) |
| unambiguous semidirect product | C17⋊(C5×D5×C19) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C2 |
| derived | C5×C17 ⋊ C2×C5×C19 |
| Hall | C52×C19 ⋊ D17 |
| Hall | C52×C17 ⋊ C2×C19 |
| Hall | C17×C19 ⋊ C5×D5 |
| Sylow | C52 ⋊ C19×D17 |
| Sylow | C17 ⋊ C5×D5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | D85 |
| commutator, cosocle, hypocenter | C5×C17 | C2×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C5×C19 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3230 |
4180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D85, C5×D5×C19×D17, C5×D85⋊D19, … |
| maximal normal subgroup of | C5×D19×D85, C5×D5×C19×D17, C5×D85⋊D19, … |
| maximal quotient of | C5×C19×Dic85, C2×C5×C19×D85 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 15);