Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1909 ⋊ C2 |
| Sylow | C7 ⋊ #21784 |
1278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,f^c=fh,g^c=gh,i^c=i^6,g^d=gh,i^d=i^6133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 178771);