Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#1279 ⋊ C2 |
| Sylow | C7 ⋊ #10348 |
588 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=d,b^2=d,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^6,c^b=cf,e^b=eh,f^b=fh,e^c=eg,f^c=fh,i^c=i^6214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 72579);