Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D7)⋊C16 |
| Fitting | C7×C22⋊C16 ⋊ C2 |
| Sylow | C7 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,h^c=h^6200 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D7×C16, C2×(C22⋊D7)⋊C16, #13506963, … |
| maximal normal subgroup of | D4×D7×C16, C2×(C22⋊D7)⋊C16, #13506963, … |
| maximal quotient of | #13265498, #13265559, #13265565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1621);