Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D7×#361 |
| Fitting | C7×#361 ⋊ C2 |
| Sylow | C7 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D7×#361, D7×#2148, #13506759, … |
| maximal normal subgroup of | C2×D7×#361, D7×#2148, #13506759, … |
| maximal quotient of | D7×#1333, #13263569, #13263800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1775);