Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1501 ⋊ C2 |
| Sylow | C7 ⋊ #17542 |
1574 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=f,d^2=h,e^2=h,b^a=be,c^a=cg,e^a=eg,e^b=eh,f^b=fgh,i^c=i^6178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 136728);