Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C9×AGL(1,ℤ/9) |
| Fitting | C22×C9×3−1+2 ⋊ C2 |
| derived | C9 ⋊ C23×C3×C9 |
| Sylow | C9×3−1+2 ⋊ C23 |
590 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D9×AGL(1,ℤ/9), C2×C9×#611⋊C3, C2×#14516793 |
| maximal normal subgroup of | C22×D9×AGL(1,ℤ/9), C2×C9×#611⋊C3, C2×#14516793 |
| maximal quotient of | C2×C9×#611⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2856);