Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1615 |
| unambiguous semidirect product | C17⋊(C5⋊D95) |
| unambiguous semidirect product | C19⋊(C5⋊D85) |
| Fitting, socle, derived, Hall | C52×C17×C19 ⋊ C2 |
| Hall | C52×C19 ⋊ D17 |
| Hall | C52×C17 ⋊ D19 |
| Hall | C17×C19 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D323 |
| Sylow | C19 ⋊ C5⋊D85 |
| Sylow | C17 ⋊ C5⋊D95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C17×C19 | C2 |
| LCS | G ▷ C52×C17×C19 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
Polycyclic presentation:
2,5^2,17,19|b^a=b^4,c^a=c^4,d^a=d^16,e^a=e^184039 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1615, D85×D95, D19×C5⋊D85, … |
| maximal normal subgroup of | D5×D1615, D85×D95, D19×C5⋊D85, … |
| maximal quotient of | C19⋊#13133334, C2×C5⋊D1615 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 10);