Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×Q32 ⋊ C2 |
| Sylow | C7 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,h^b=h^6,e^c=eg,h^c=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2195, C2×#11729260, #13507751, … |
| maximal normal subgroup of | D7×#2195, C2×#11729260, #13507751, … |
| maximal quotient of | #13265947, #13265954, #13266291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4026);