Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #13817 |
1970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=h,c^2=g,d^2=fg,b^a=be,c^a=cf,i^a=i^6,d^b=de,i^d=i^6340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 91109);