Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1675 |
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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=fg,b^2=df,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^6,e^c=eg149 conjugacy classes — view the full character table.
| maximal subgroup of | #13267604, #13267606, #13267611, … |
| maximal normal subgroup of | #13267604, #13267606, #13267611, … |
| maximal quotient of | #13246850, #13249935, #13252151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3373);