Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C7×#1282 ⋊ C2 |
| Sylow | C7 ⋊ #8161 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,c^2=e,e^2=h,b^a=bd,c^a=ch,f^a=fg,d^b=dg,i^b=i^6,i^c=i^6196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 60120);