Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#1996 ⋊ C2 |
| Sylow | C7 ⋊ #9255 |
924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=df,d^2=gh,e^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^6,d^b=dh,e^b=egh,f^b=fh,i^b=i^6,d^c=dgh,e^c=egh,f^c=fgh,i^c=i^6139 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 65990);