Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #8374 |
712 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=g,c^2=gh,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,f^b=fgh,f^c=fg,i^c=i^6139 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 61223);