Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#2966 ⋊ C2 |
| Sylow | C7 ⋊ #60307 |
1820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,e^2=g,g^2=h,b^a=bf,c^a=ch,d^a=df,c^b=cfh,d^b=dh,i^c=i^6,i^d=i^6244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1035262);