Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #1873 |
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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:
2^7,7|a^2=f,b^2=df,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^6,d^b=dg,f^b=fg158 conjugacy classes — view the full character table.
| maximal subgroup of | #13246131, #13246132, D7×#1873, … |
| maximal normal subgroup of | #13246131, #13246132, D7×#1873, … |
| maximal quotient of | #13248322, #13248337, #13248536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4105);