Finite Group DatabasebetaFinite Group Databasebeta| order | 17050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D275 |
| unambiguous semidirect product | C11⋊(C31×D25) |
| unambiguous semidirect product | C25⋊(D11×C31) |
| Fitting, Hall | C11×C25×C31 ⋊ C2 |
| derived, Hall | C11×C25 ⋊ C2×C31 |
| Hall | C25×C31 ⋊ D11 |
| Hall | C11×C31 ⋊ D25 |
| Sylow | C25 ⋊ D11×C31 |
| Sylow | C11 ⋊ C31×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D275 |
| commutator, cosocle, hypocenter | C11×C25 | C2×C31 |
| Frattini | C5 | C31×D55 |
| Fitting | C11×C25×C31 | C2 |
| socle | C5×C11×C31 | D5 |
| LCS | G ▷ C11×C25 | |
| UCS | C1 ◁ C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8525 |
4309 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D275, D11×C31×D25, D275⋊D31, … |
| maximal normal subgroup of | D31×D275, D11×C31×D25, D275⋊D31, … |
| maximal quotient of | C31×Dic275, C2×C31×D275 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17050, 13);