Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C7 ⋊ #12594 |
354 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 203 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=e,b^2=f,c^2=d,d^2=h,e^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^6,c^b=ch,e^b=eh328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 84580);