Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#89620 |
| Fitting | C2×C7×C4⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#460 |
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
158 conjugacy classes — view the full character table.
| maximal subgroup of | #13248563, #13248565, #13248570, … |
| maximal normal subgroup of | #13248563, #13248565, #13248570, … |
| maximal quotient of | C2×#11726300, C2×#11726340, C2×#11726341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11242);