Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #12084 |
220 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 77 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=e,c^2=e,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=cgh,d^a=df,f^a=fh,i^a=i^6,c^b=cg,d^b=df,f^b=fh184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 81564);