Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C7×#2982 ⋊ C2 |
| Sylow | C7 ⋊ C8×2−1+4 |
2190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=f,c^2=f,e^2=g,g^2=h,b^a=bf,d^a=df,c^b=cf,i^e=i^6340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1035601);