Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | D7×C22⋊C16 |
| Fitting | C7×C22⋊C16 ⋊ C2 |
| Sylow | C7 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1314, #13262859, D7×#1315, … |
| maximal normal subgroup of | D7×#1314, #13262859, D7×#1315, … |
| maximal quotient of | D7×#1314, D7×#1322, #13262991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1625);