Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C7×#2016 ⋊ C2 |
| Sylow | C7 ⋊ #23432 |
2018 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|b^2=h,c^2=h,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^6,c^b=cg,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,f^c=fh,i^d=i^6148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 196739);