Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#4294⋊AGL(1,𝔽5) |
| unambiguous semidirect product | #4294⋊(C5×AGL(1,𝔽5)) |
| derived | C5×C19 ⋊ C4×C5×C9 |
| Hall | C52×#4294 ⋊ C4 |
| Hall | C5×C19⋊AGL(1,𝔽5) ⋊ C9 |
| Hall | C52×C19 ⋊ C4×C9 |
| Hall | #4294 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C5×C9×AGL(1,𝔽5) |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3420 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 171);