Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C3⋊(#1043⋊C3) |
| unambiguous semidirect product | C3⋊(C19×#1043⋊C3) |
| unambiguous semidirect product | (C3⋊#1043)⋊(C3×C19) |
| Fitting, socle | C3×C52×C19 ⋊ C3×C4 |
| derived | C3×C52 ⋊ C3×C4×C19 |
| Hall | C3×C19×C52⋊C3 ⋊ C4 |
| Hall | C52×C19 ⋊ C3×Dic3 |
| Hall | C3×C52⋊C3 ⋊ C4×C19 |
| Sylow | C52 ⋊ C3×Dic3×C19 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 434);