Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #7024 |
468 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=d,b^2=e,c^2=fg,d^2=h,e^2=fgh,b^a=bc,c^a=cf,e^a=efg,i^a=i^6,d^b=dg,i^b=i^6232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 56118);