Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#6374 |
| Fitting | C4×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
236 conjugacy classes — view the full character table.
| maximal subgroup of | #13265522, C8×#6374, #13265534, … |
| maximal normal subgroup of | #13265522, C8×#6374, #13265534, … |
| maximal quotient of | C8×#6374, #13265700, #13265707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1583);