Finite Group DatabasebetaFinite Group Databasebeta| order | 15650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1565 |
| unambiguous semidirect product | C5⋊(C5×D313) |
| unambiguous semidirect product | C313⋊(C5×D5) |
| Fitting, socle, Hall | C52×C313 ⋊ C2 |
| derived | C5×C313 ⋊ C2×C5 |
| Sylow | C313 ⋊ C5×D5 |
| Sylow | C52 ⋊ D313 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1565 |
| commutator, cosocle, hypocenter | C5×C313 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C313 | C2 |
| LCS | G ▷ C5×C313 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3130 |
3920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D5×D313, C5×#20262405, C5×#20262406, … |
| maximal normal subgroup of | C5×D5×D313, C5×#20262405, C5×#20262406, … |
| maximal quotient of | C5×Dic1565, C2×C5×D1565 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15650, 8);