Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C7⋊#1309 |
| Sylow | C7 ⋊ #1309 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=eg,h^a=h^6,c^b=cg,d^b=df110 conjugacy classes — view the full character table.
| maximal subgroup of | #13241339, #13241340, #13241417, … |
| maximal normal subgroup of | #13241339, #13241340, #13241417, … |
| maximal quotient of | #13240371, #13240372, #13240392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 284);