Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D25×AGL(1,𝔽19) |
| unambiguous semidirect product | (C25×AGL(1,𝔽19))⋊C2 |
| unambiguous semidirect product | (D25×#4296)⋊C2 |
| unambiguous semidirect product | (C25⋊AGL(1,𝔽19))⋊C2 |
| Fitting, derived, Hall | C19×C25 ⋊ C22×C9 |
| Hall | C25×#4296 ⋊ C22 |
| Hall | D19×D25 ⋊ C9 |
| Hall | #4296 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×AGL(1,𝔽19) |
| Sylow | C19 ⋊ C2×C9×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C19×C25 | C22×C9 |
| Frattini | C5 | D5×AGL(1,𝔽19) |
| socle | C5×C19 | C2×C9×D5 |
| prime radical | D25×D19⋊C3 | C3 |
| cosocle | C25×C19⋊C3 | C22×C3 |
| LCS | G ▷ C19×C25 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 475 |
266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 96);