Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#336 ⋊ C2 |
| Sylow | C7 ⋊ #1869 |
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,b^2=df,f^2=g,b^a=bd,c^a=ce,h^a=h^6,h^c=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1869, C2×#11726422, #13354922, … |
| maximal normal subgroup of | D7×#1869, C2×#11726422, #13354922, … |
| maximal quotient of | #13248316, #13248321, #13248326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1188);