Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #10407 |
576 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 115 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|a^2=g,b^2=g,c^2=dg,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^6,c^b=cf,e^b=eh,f^b=fg,i^b=i^6,e^c=eg,f^c=fg172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 72921);