Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C19 · Schur multiplier (H2) = C5 |
| direct product | C52×C19×D17 |
| unambiguous semidirect product | C17⋊(C2×C52×C19) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C52×C19 |
| Hall | C52×C17 ⋊ C2×C19 |
| Hall | C17×C19 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C19 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C52×C19 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C52×C19 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
4750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×C19×#595, C52×C19⋊#595, C52×D17×D19, … |
| maximal normal subgroup of | C52×C19×#595, C52×C19⋊#595, C52×D17×D19, … |
| maximal quotient of | C52×C19×Dic17, C2×C52×C19×D17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 19);