Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #7680 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,c^2=fg,d^2=g,e^2=h,b^a=bd,c^a=cf,d^a=df,i^a=i^6,c^b=ch,d^b=dg,e^b=efg,i^b=i^6226 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 58021);