Finite Group DatabasebetaFinite Group Databasebeta| order | 17090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1709 |
| unambiguous semidirect product | C1709⋊(C2×C5) |
| Fitting, socle, Hall | C5×C1709 ⋊ C2 |
| derived, Sylow | C1709 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1709 |
| commutator, cosocle, hypocenter | C1709 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1709 | C2 |
| LCS | G ▷ C1709 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8545 |
4280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20292020, #46803102, D5×D1709, … |
| maximal normal subgroup of | C5×#20292020, #46803102, D5×D1709, … |
| maximal quotient of | C5×Dic1709, C2×C5×D1709 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17090, 2);