Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#1043⋊(C19⋊C3) |
| unambiguous semidirect product | (C3×#1043)⋊(C19⋊C3) |
| Fitting, socle | C3×C52×C19 ⋊ C3×C4 |
| derived, Hall | C52×C19 ⋊ C32×C4 |
| Hall | C3×C19⋊(C52⋊C3) ⋊ C4 |
| Hall | C19×#1043 ⋊ C32 |
| Hall | #1043 ⋊ C3×C19⋊C3 |
| Sylow | C52 ⋊ C3×C4×C19⋊C3 |
| Sylow | C19 ⋊ C3×#1043⋊C3 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 390);