Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C7⋊C32) |
| Sylow | C7 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | #13241134, #13241135, #13241136, … |
| maximal normal subgroup of | #13241134, #13241135, #13241136, … |
| maximal quotient of | #13241135, #13241195, D4⋊(C7⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 375);