Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2176 |
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 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) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=g,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^6,d^b=df,f^b=fg116 conjugacy classes — view the full character table.
| maximal subgroup of | #13265673, #13265674, #13265758, … |
| maximal normal subgroup of | #13265673, #13265674, #13265758, … |
| maximal quotient of | #13265540, #13265738, #13265740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3429);