Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #1466 |
300 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,c^2=fg,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^6,e^b=ef152 conjugacy classes — view the full character table.
| maximal subgroup of | #13240908, #13240909, #13241101, … |
| maximal normal subgroup of | #13240908, #13240909, #13241101, … |
| maximal quotient of | #13241984, #13241998, #13242011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4123);