Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#504 ⋊ C2 |
| Sylow | C7 ⋊ #2171 |
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,d^a=dg,h^a=h^6,d^b=dg164 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2171, C2×#11729207, #13507034, … |
| maximal normal subgroup of | D7×#2171, C2×#11729207, #13507034, … |
| maximal quotient of | #13265504, #13265506, #13265567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3973);