Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #11506 |
598 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 95 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=e,b^2=h,d^2=h,e^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,d^b=dh,e^b=efh,i^b=i^6,e^d=eh136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 78947);