Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#508 ⋊ C2 |
| Sylow | C7 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^6,e^b=ef,f^b=fg,h^b=h^6,d^c=dg,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13274484, #13274488, #13274498, … |
| maximal normal subgroup of | #13274484, #13274488, #13274498, … |
| maximal quotient of | #13506711, #13506837, #13507142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14244);