Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#2115 ⋊ C2 |
| Sylow | C7 ⋊ #33337 |
1128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=f,f^2=g,g^2=h,b^a=be,e^a=eh,f^b=fh,i^b=i^6,d^c=dh,i^d=i^6214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 322261);