Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#2223 ⋊ C2 |
| Sylow | C7 ⋊ #33619 |
636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=eg,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,g^a=gh,d^b=dh,i^b=i^6,f^c=fh,i^d=i^6124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 324161);