Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C7×#413 ⋊ C2 |
| Sylow | C7 ⋊ #20618 |
3690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,d^2=h,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^6,e^b=eh,f^b=fh,i^b=i^6,e^c=eh190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 168886);