Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#2406 ⋊ C2 |
| Sylow | C7 ⋊ #32901 |
3706 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 3706 conjugacy classes of subgroups — too many to draw. Only its 251 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=h,d^2=h,b^a=be,c^a=cf,d^a=dg,f^b=fh,e^c=eh,i^c=i^6163 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 318353);