Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #33312 |
1006 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 395 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=e,b^2=e,c^2=fh,d^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,f^a=fh,i^c=i^6208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 322142);