Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | D7×#405 |
| Fitting | C7×#405 ⋊ C2 |
| Sylow | C7 ⋊ C2×#405 |
592 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1378, D7×#1379, #13268667, … |
| maximal normal subgroup of | D7×#1378, D7×#1379, #13268667, … |
| maximal quotient of | C8×D7×M16, D7×#1450, D7×#1451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10758);