Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×C617 ⋊ C2 |
| Sylow | C617 ⋊ SD32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9872 |
Polycyclic presentation:
2^5,617|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^6162167 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 89);