Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1746 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^6,c^b=cg,h^b=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | #13244252, #13244257, #13244841, … |
| maximal normal subgroup of | #13244252, #13244257, #13244841, … |
| maximal quotient of | #13244221, #13244226, #13244229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2326);