Finite Group DatabasebetaFinite Group Databasebeta| order | 17050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×#22555291 |
| derived, Hall | C11×C31 ⋊ C2×C25 |
| Hall | C2×C11×C31 ⋊ C25 |
| Hall | C2×C31 ⋊ C11⋊C25 |
| Sylow | C31 ⋊ C2×C11⋊C25 |
| Hall | C2×C11 ⋊ C31⋊C25 |
| Sylow | C11 ⋊ C2×C31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #13133721 |
| commutator, hypocenter | C11×C31 | C2×C25 |
| Frattini | C5 | C2×#13133721 |
| Fitting, socle, prime radical | C2×C5×C11×C31 | C5 |
| cosocle | C5×C11×C31 | C2×C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17050 |
730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22555291, #46801926, #46801932, … |
| maximal normal subgroup of | C4×#22555291, #46801926, #46801932, … |
| maximal quotient of | C4×#22555291, C22×#22555291 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17050, 4);