Finite Group DatabasebetaFinite Group Databasebeta| order | 16150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×C5⋊D95 |
| unambiguous semidirect product | C5⋊(C17×D95) |
| unambiguous semidirect product | C19⋊(C17×C5⋊D5) |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C2 |
| derived, Hall | C52×C19 ⋊ C2×C17 |
| Hall | C52×C17 ⋊ D19 |
| Hall | C17×C19 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C17×D19 |
| Sylow | C19 ⋊ C17×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C5⋊D95 |
| commutator, cosocle, hypocenter | C52×C19 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C2 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
4063 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C17×D95, D85⋊D95, C17×D19×C5⋊D5, … |
| maximal normal subgroup of | D5×C17×D95, D85⋊D95, C17×D19×C5⋊D5, … |
| maximal quotient of | C17×C19⋊#1039, C2×C17×C5⋊D95 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16150, 12);