Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D7×AGL(1,ℤ/8) |
| Fitting | C2×C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1883, #13355324, D7×#1903, … |
| maximal normal subgroup of | D7×#1883, #13355324, D7×#1903, … |
| maximal quotient of | C2×D7×#418, C2×D7×#417, C2×D7×#428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19022);