Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C7×#344 ⋊ C2 |
| Sylow | C7 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^6110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1757, C2×#11726768, #13351498, … |
| maximal normal subgroup of | D7×#1757, C2×#11726768, #13351498, … |
| maximal quotient of | #13244323, #13244327, #13244331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1534);