Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#89639 |
| Fitting | C2×C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ C2×#485 |
416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #13360963, C4×#89639, #13361037, … |
| maximal normal subgroup of | #13360963, C4×#89639, #13361037, … |
| maximal quotient of | C2×#11726567, C2×#11728334, C2×#11726633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11322);