Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic7×D16 |
| Sylow | C7 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #13274367, Dic7×D32, Dic7×SD64, … |
| maximal normal subgroup of | #13274367, Dic7×D32, Dic7×SD64, … |
| maximal quotient of | D16×C7⋊C8, #13265692, #13265775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3980);