Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#1992 ⋊ C2 |
| Sylow | C7 ⋊ #8507 |
736 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=g,d^2=h,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^6,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,e^c=eg,f^c=fg,i^c=i^6136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 62015);