Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1986 |
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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=f,b^2=de,c^2=ef,d^2=g,b^a=bd,c^a=cef,d^b=dg,e^b=eg,f^b=fg,h^c=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1986, C2×#11726484, #13358280, … |
| maximal normal subgroup of | D7×#1986, C2×#11726484, #13358280, … |
| maximal quotient of | #13253775, #13253779, #13253783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1250);