Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#89628 |
| Sylow | C7 ⋊ C2×#501 |
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#89628, #13362607, #13362615, … |
| maximal normal subgroup of | C4×#89628, #13362607, #13362615, … |
| maximal quotient of | C2×#11728310, C2×#11728315, C2×#11726614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11320);