Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #13460 |
310 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=d,b^2=d,c^2=dg,e^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,g^a=gh,i^a=i^6,c^b=cf,f^b=fh,d^c=dh,e^c=eg,g^c=gh130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 89231);