Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C7×#131 ⋊ C2 |
| Sylow | C7 ⋊ #60219 |
1906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=g,d^2=f,g^2=h,b^a=bf,c^a=ch,e^a=eh,i^a=i^6,e^b=eh,e^d=eh328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1034282);