Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #7067 |
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=d,b^2=e,c^2=h,d^2=f,f^2=h,b^a=bc,c^a=ce,e^a=eg,c^b=cgh,d^b=deh,i^b=i^6,d^c=dg178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 56213);