Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | 3−1+2×#625 |
| unambiguous semidirect product | (C9×#625)⋊C3 |
| Sylow | C32×3−1+2 ⋊ D4 |
576 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | #72229040, #72259522, D3×#67×3−1+2, … |
| maximal normal subgroup of | #72259522, D3×#67×3−1+2, #72259642 |
| maximal quotient of | #72229040 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3035);