Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#1380 ⋊ C2 |
| Sylow | C7 ⋊ #12557 |
630 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,d^2=gh,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,c^b=ch,i^c=i^6196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 84449);