Finite Group DatabasebetaFinite Group Databasebeta| order | 15950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1595 |
| unambiguous semidirect product | C5⋊(C5×D319) |
| unambiguous semidirect product | C29⋊(C5×D55) |
| Fitting, socle, Hall | C52×C11×C29 ⋊ C2 |
| derived | C5×C11×C29 ⋊ C2×C5 |
| Hall | C52×C29 ⋊ D11 |
| Hall | C11×C29 ⋊ C5×D5 |
| Hall | C52×C11 ⋊ D29 |
| Sylow | C29 ⋊ C5×D55 |
| Sylow | C52 ⋊ D319 |
| Sylow | C11 ⋊ C5×D145 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1595 |
| commutator, cosocle, hypocenter | C5×C11×C29 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C29 | C2 |
| LCS | G ▷ C5×C11×C29 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3190 |
3995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D29×D55, C5×D11×D145, C5×D5×D319, … |
| maximal normal subgroup of | C5×D29×D55, C5×D11×D145, C5×D5×D319, … |
| maximal quotient of | C5×Dic1595, C2×C5×D1595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15950, 26);