Finite Group DatabasebetaFinite Group Databasebeta| order | 10170 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C113 · Schur multiplier (H2) = C1 |
| direct product | C9×D5×C113 |
| unambiguous semidirect product | C5⋊(C2×C9×C113) |
| Fitting, Hall | C5×C9×C113 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C9×C113 |
| Hall | C5×C113 ⋊ C2×C9 |
| Hall | C5×C9 ⋊ C2×C113 |
24 conjugacy classes of subgroups.
4068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×AGL(1,𝔽5)×C113, C9×#14555935, C9×D5×D113, … |
| maximal normal subgroup of | C9×AGL(1,𝔽5)×C113, C9×#14555935, C9×D5×D113, … |
| maximal quotient of | C9×Dic5×C113, C2×C9×D5×C113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10170, 3);