Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C7×H(3,ℤ/4) ⋊ C2 |
| Sylow | C7 ⋊ #11013 |
1262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^6,c^b=cf,f^b=fh,g^b=gh,i^b=i^6,f^c=fh,i^c=i^6178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 76307);