Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C16×C22⋊D7 |
| Fitting | C22×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C22⋊D7)⋊C32, C32×C22⋊D7, #13274345, … |
| maximal normal subgroup of | (C22⋊D7)⋊C32, C32×C22⋊D7, #13274345, … |
| maximal quotient of | C16×#1141, C16×#1142, C16×#1143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3926);