Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1898 ⋊ C2 |
| Sylow | C7 ⋊ #24405 |
1698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=fh,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,f^b=fh,i^b=i^6,e^c=eh,i^c=i^6,f^d=fh,i^d=i^6139 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 206919);