Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C32×#611⋊C3 |
| unambiguous semidirect product | #611⋊C33 |
| unambiguous semidirect product | (C3×#611)⋊C32 |
| Fitting | C22×C32×3−1+2 ⋊ C2 |
| Sylow | C32×3−1+2 ⋊ D4 |
1182 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#14517439, 3−1+2×#611⋊C3, C3×#88668⋊C3, … |
| maximal normal subgroup of | C3×#14517439, 3−1+2×#611⋊C3, C3×#88668⋊C3, … |
| maximal quotient of | C3×#14517439, 3−1+2×#611⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3297);