Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C7⋊#1273 |
| Sylow | C7 ⋊ #1273 |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^a=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | #13240568, #13240569, #13240581, … |
| maximal normal subgroup of | #13240568, #13240569, #13240581, … |
| maximal quotient of | C7⋊#7014, #13240323, #13240324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 225);