Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#6512 |
| Fitting | C22×C7×#41 ⋊ C2 |
| Sylow | C7 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #13260522, #13260526, #13260537, … |
| maximal normal subgroup of | #13260522, #13260526, #13260537, … |
| maximal quotient of | C22×#89773, C22×#90004, C22×#89767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19089);