Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D7×#106 |
| Fitting | C2×C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ C22×#106 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1383, D7×#1386, #13270351, … |
| maximal normal subgroup of | D7×#1383, D7×#1386, #13270351, … |
| maximal quotient of | C2×D7×#334, D7×#1566, C2×#11726283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11324);