Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#6407 |
| Sylow | C7 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #13240790, #13240791, #13241005, … |
| maximal normal subgroup of | #13240790, #13240791, #13241005, … |
| maximal quotient of | C4×#89320, #13244306, #13244319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4136);