Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#1279 ⋊ C2 |
| Sylow | C7 ⋊ C4×D4⋊C8 |
774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,c^2=e,d^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fg,i^c=i^6280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 60159);