Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×D4×M16 ⋊ C2 |
| Sylow | C7 ⋊ #60231 |
2242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=g,g^2=h,b^a=bf,d^a=df,e^a=eh,c^b=cf,d^b=dh,i^d=i^6226 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1034363);