Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#335 ⋊ C2 |
| Sylow | C7 ⋊ #1331 |
110 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 45 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=d,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=ce,e^b=eg,h^b=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1331, C2×#11725277, #13263534, … |
| maximal normal subgroup of | D7×#1331, C2×#11725277, #13263534, … |
| maximal quotient of | #13240444, #13240456, #13240562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 43);