Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#1143 |
| Fitting | C7×C8×Q8 ⋊ C2 |
| Sylow | C7 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13265559, C16×#1143, #13265566, … |
| maximal normal subgroup of | #13265559, C16×#1143, #13265566, … |
| maximal quotient of | C8×#6383, C8×#6409, C8×#6382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3450);