Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#89246 |
| Fitting | C2×C7×#95 ⋊ C2 |
| Sylow | C7 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
158 conjugacy classes — view the full character table.
| maximal subgroup of | #13244669, C4×#89246, #13244679, … |
| maximal normal subgroup of | #13244669, C4×#89246, #13244679, … |
| maximal quotient of | C2×#11725285, C2×#11725284, #13241753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1917);