Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#89331 |
| Sylow | C7 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#89331, Dic7×AΣL(1,𝔽16), #13268943, … |
| maximal normal subgroup of | C4×#89331, Dic7×AΣL(1,𝔽16), #13268943, … |
| maximal quotient of | C2×#11725428, C2×#11725442, #13263046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4188);