Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#2222 ⋊ C2 |
| Sylow | C7 ⋊ #33855 |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=h,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,g^a=gh,d^b=de,e^b=eg,g^b=gh,i^b=i^6,f^c=fh,e^d=eg,g^d=gh,i^d=i^6115 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 326326);