Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#14578674)⋊C4 |
| Fitting | C2×C4×C617 ⋊ C4 |
| Sylow | C617 ⋊ #95 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4936 |
Polycyclic presentation:
2^5,617|a^2=d,b^2=e,b^a=bc,f^a=f^194,f^d=f^6161252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 197);