Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #8231 |
684 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,c^2=e,d^2=g,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,i^a=i^6,c^b=cg,d^b=dh,i^c=i^6166 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 60523);