Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C9×((C3⋊D3)⋊C3)⋊C2 |
| unambiguous semidirect product | ((C3⋊D3)⋊C3)⋊(C22×C9) |
| Fitting | C2×C9×H(3,𝔽3) ⋊ C22 |
| derived | H(3,𝔽3) ⋊ C23×C9 |
| Sylow | C9×H(3,𝔽3) ⋊ C23 |
488 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221858, C2×#72221863 |
| maximal quotient of | C2×#72221861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2680);