Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C7×#95 ⋊ C2 |
| Sylow | C7 ⋊ #11053 |
1070 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=d,e^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^6,c^b=cf,e^c=eh,i^c=i^6304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 76543);