Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #22277 |
826 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 259 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=egh,c^2=efh,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^6,c^b=ce,d^b=dh,i^b=i^6184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 183419);