Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D56 |
| Fitting | C7×C8×Q8 ⋊ C2 |
| Sylow | C7 ⋊ Q8×D8 |
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | #13267470, #13267474, #13267498, … |
| maximal normal subgroup of | #13267470, #13267474, #13267498, … |
| maximal quotient of | Q8×#6395, C4⋊C4×D56, Q8×#6392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12139);