Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#2198 ⋊ C2 |
| Sylow | C7 ⋊ #33557 |
1258 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^8,7|b^a=be,c^a=cf,g^a=gh,d^b=dh,f^b=fgh,i^b=i^6,d^c=dh,e^c=eg,i^c=i^6,i^d=i^6,f^e=fh94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 323684);