Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#89253 |
| Sylow | C7 ⋊ C2×#335 |
200 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 200 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) = 896 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #13240665, #13240666, #13240677, … |
| maximal normal subgroup of | #13240665, #13240666, #13240677, … |
| maximal quotient of | C2×#11725460, C4×#89253, #13246635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2248);