Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1392 |
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,d^2=g,e^2=g,b^a=bc,c^a=cf,f^a=fg,h^a=h^6,d^b=df,d^c=dg110 conjugacy classes — view the full character table.
| maximal subgroup of | #13241297, #13241298, #13241300, … |
| maximal normal subgroup of | #13241297, #13241298, #13241300, … |
| maximal quotient of | #13240757, #13240791, #13240830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 265);