Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1298 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | #13241288, #13241289, #13241396, … |
| maximal normal subgroup of | #13241288, #13241289, #13241396, … |
| maximal quotient of | #13240349, #13240357, #13240381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 260);