Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#1306 ⋊ C2 |
| Sylow | C7 ⋊ #8115 |
914 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 155 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=f,c^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fh,c^b=ch,d^b=dh,e^b=eg,i^c=i^6130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 59941);