Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#6470 |
| Fitting | C22×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C22×#131 |
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13259209, #13259213, #13259227, … |
| maximal normal subgroup of | #13259209, #13259213, #13259227, … |
| maximal quotient of | C22×#89480, C22×#89894, C2×C4×#6470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18987);