Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×C7⋊C16 |
| Sylow | C7 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13265498, D8×C7⋊C16, #13265503, … |
| maximal normal subgroup of | #13265498, D8×C7⋊C16, #13265503, … |
| maximal quotient of | D8×C7⋊C16, SD16×C7⋊C16, Q16×C7⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3376);