Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#1311 ⋊ C2 |
| Sylow | C7 ⋊ #11408 |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=d,b^2=e,d^2=f,e^2=g,g^2=h,b^a=bh,c^a=cf,i^c=i^6352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 78584);