Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C7×#3020 ⋊ C2 |
| Sylow | C7 ⋊ #60390 |
4698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|c^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,f^b=fh,g^b=gh,f^c=fh,i^c=i^6,e^d=eh,i^d=i^6,i^e=i^6145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1036265);