Finite Group DatabasebetaFinite Group Databasebeta| order | 1904 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C7⋊#595) |
| Fitting | C4×C7×C17 ⋊ C4 |
| Hall | C7×C17 ⋊ C4⋊C4 |
| Sylow | C17 ⋊ C4⋊Dic7 |
| Sylow | C7 ⋊ C4⋊#595 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 476 |
Polycyclic presentation:
2^4,7,17|a^2=c,b^2=d,b^a=bd,e^a=e^6,f^a=f^13,f^c=f^16146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1904, 107);