Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C7⋊C16) |
| Sylow | C7 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^6,c^b=ce176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×Q8⋊C16, C2×Q8⋊(C7⋊C16), #13263597, … |
| maximal normal subgroup of | D7×Q8⋊C16, C2×Q8⋊(C7⋊C16), #13263597, … |
| maximal quotient of | #13240578, #13240608, #13240700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 340);