Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C7×#432 ⋊ C2 |
| Sylow | C7 ⋊ #60211 |
1952 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=g,d^2=f,g^2=h,b^a=bf,d^a=dh,e^c=eh,i^c=i^6256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1034155);