Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D323 |
| unambiguous semidirect product | C17⋊(C52×D19) |
| unambiguous semidirect product | C19⋊(C52×D17) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C2 |
| derived, Hall | C17×C19 ⋊ C2×C52 |
| Hall | C52×C19 ⋊ D17 |
| Hall | C52×C17 ⋊ D19 |
| Sylow | C19 ⋊ C52×D17 |
| Sylow | C17 ⋊ C52×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D323 |
| commutator, cosocle, hypocenter | C17×C19 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C2 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
4075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D17×D19, C5×D5×D323, C5×D85⋊D19, … |
| maximal normal subgroup of | C52×D17×D19, C5×D5×D323, C5×D85⋊D19, … |
| maximal quotient of | C52×Dic323, C2×C52×D323 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 18);