Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#6439 |
| Fitting | C43×C7 ⋊ C2 |
| Sylow | C7 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #13362006, C8×#6439, #13362013, … |
| maximal normal subgroup of | #13362006, C8×#6439, #13362013, … |
| maximal quotient of | C4×#89712, C4×#89705, C4×#89709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5514);