Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D7×#357 |
| Fitting | C7×#357 ⋊ C2 |
| Sylow | C7 ⋊ C2×#357 |
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D7×#357, D7×#2138, D7×#2140, … |
| maximal normal subgroup of | C2×D7×#357, D7×#2138, D7×#2140, … |
| maximal quotient of | D7×#1331, #13263769, #13263821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1707);