Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2083 |
230 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=d,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^6,c^b=cf,f^b=fg,f^c=fg116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2083, C2×#11728373, #13382779, … |
| maximal normal subgroup of | D7×#2083, C2×#11728373, #13382779, … |
| maximal quotient of | #13258705, #13258710, #13258725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3139);