Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#3199 ⋊ C2 |
| Sylow | C7 ⋊ #60753 |
2322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|g^2=h,b^a=bf,c^a=cg,d^a=df,e^a=eh,g^a=gh,c^b=cf,d^b=dh,g^c=gh,i^d=i^6,i^e=i^6124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1040349);