Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1463 ⋊ C2 |
| Sylow | C7 ⋊ #18142 |
1450 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 167 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|c^2=h,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,i^a=i^6,e^b=eg,f^b=fh,i^b=i^6,e^c=eh133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 142019);