Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #12667 |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,c^2=de,e^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^6,c^b=cg,d^b=dh,i^b=i^6,f^c=fh,i^c=i^6232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 84945);