Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic6×C27 |
| unambiguous semidirect product | C3⋊(C3×Q8×C27) |
| Sylow | C32×C27 ⋊ Q8 |
234 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1729);