Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#366 ⋊ C2 |
| Sylow | C7 ⋊ #2159 |
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,b^2=df,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2159, C2×#11727080, #13506832, … |
| maximal normal subgroup of | D7×#2159, C2×#11727080, #13506832, … |
| maximal quotient of | #13265382, #13265446, #13265488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1846);