Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1729 ⋊ C2 |
| Sylow | C7 ⋊ #20839 |
1458 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^6,i^b=i^6,d^c=dh,i^c=i^6244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 170269);