Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C9×3−1+2⋊C4 |
| derived | C9 ⋊ C2×C3×C4×C9 |
| Sylow | C9×3−1+2 ⋊ C2×C4 |
350 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 145 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 | C2×#92299⋊C4, C2×C9×#611⋊C3 |
| maximal normal subgroup of | C2×#92299⋊C4, C2×C9×#611⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1812);