Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D52×#4296 |
| unambiguous semidirect product | (C5×D5)⋊(C2×#4296) |
| Fitting, socle, derived, Hall | C52×C19 ⋊ C22×C9 |
| Hall | C52×#4296 ⋊ C22 |
| Hall | D52×C19 ⋊ C9 |
| Sylow | C52 ⋊ C22×#4296 |
| Sylow | C19 ⋊ C9×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C19 | C22×C9 |
| prime radical | D52×C19⋊C3 | C3 |
| cosocle | C52×C19⋊C3 | C22×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 345);