Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #11414 |
248 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=bg,c^a=cf,e^a=eh,c^b=ch,d^b=dh,i^b=i^6232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 78615);