Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×Q8⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^6,d^b=df,h^b=h^6,h^c=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | D7×SD16⋊C8, C2×#11725968, #13323198, … |
| maximal normal subgroup of | D7×SD16⋊C8, C2×#11725968, #13323198, … |
| maximal quotient of | #13244573, #13244584, #13245044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 734);