Finite Group DatabasebetaFinite Group Databasebeta| order | 10690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1069 |
| unambiguous semidirect product | C1069⋊(C2×C5) |
| Fitting, socle, Hall | C5×C1069 ⋊ C2 |
| derived, Sylow | C1069 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1069 |
| commutator, cosocle, hypocenter | C1069 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1069 | C2 |
| LCS | G ▷ C1069 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#16862693, #36338977, D5×D1069, … |
| maximal normal subgroup of | C5×#16862693, #36338977, D5×D1069, … |
| maximal quotient of | C5×Dic1069, C2×C5×D1069, C3×C5×D1069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10690, 2);