Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | 3−1+2×#638 |
| Fitting | C22×C32×3−1+2 ⋊ C2 |
| Sylow | C32×3−1+2 ⋊ D4 |
984 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | #72229030, #72259536, #72259553, … |
| maximal normal subgroup of | #72259536, #72259553, D3×#67×3−1+2 |
| maximal quotient of | #72229030 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3353);