Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | #1035×#4296 |
| Fitting, derived, Hall | C19×C25 ⋊ C4×C9 |
| Hall | C25×#4296 ⋊ C4 |
| Hall | C19×#1035 ⋊ C9 |
| Sylow | C25 ⋊ C4×#4296 |
| Sylow | C19 ⋊ C9×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C19×C25 | C4×C9 |
| Frattini | C5 | AGL(1,𝔽5)×#4296 |
| socle | C5×C19 | C9×AGL(1,𝔽5) |
| prime radical, cosocle | D25×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C25 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 475 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 95);