Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#89420 |
| Sylow | C7 ⋊ C2×#376 |
840 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 405 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13243385, #13243397, #13243786, … |
| maximal normal subgroup of | #13243385, #13243397, #13243786, … |
| maximal quotient of | C2×Dic7×#95, C4×#89420, C2×#11727156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5530);