Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C2×C7×#405 ⋊ C2 |
| Sylow | C7 ⋊ #60058 |
3178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=g,f^2=h,e^b=eh,d^c=dh,i^d=i^6376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1032987);