Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C7×#2344 ⋊ C2 |
| Sylow | C7 ⋊ #22570 |
1218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=f,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^6,d^b=de,e^b=eh,e^d=eh,i^d=i^6220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 186710);