Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1459 ⋊ C2 |
| Sylow | C7 ⋊ #8376 |
1034 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=f,c^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,f^b=fgh,i^b=i^6,f^c=fg175 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 61234);