Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #8486 |
686 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,c^2=gh,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^6,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,f^c=fg151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 61888);