Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C7×#504 ⋊ C2 |
| Sylow | C7 ⋊ #62635 |
2038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|e^2=h,f^2=gh,g^2=h,b^a=bf,f^a=fg,g^a=gh,i^a=i^6,f^b=fg,g^b=gh,i^b=i^6,d^c=dh304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076101);