Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C7×#1749 ⋊ C2 |
| Sylow | C7 ⋊ #20487 |
1118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=g,c^2=g,d^2=f,f^2=h,b^a=be,d^a=dh,i^a=i^6,c^b=ch,i^b=i^6,i^d=i^6256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 167933);