Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C7×#1744 ⋊ C2 |
| Sylow | C7 ⋊ C8×#117 |
1174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=g,c^2=f,d^2=e,f^2=h,b^a=be,i^c=i^6400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 167769);