Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#2980 ⋊ C2 |
| Sylow | C7 ⋊ #13052 |
624 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 624 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=f,b^2=df,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=egh,g^a=gh,i^a=i^6,c^b=ch,e^b=egh,d^c=dg,e^c=eh,f^c=fg,e^d=eh,f^e=fh148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 86895);