Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C4×(C3⋊D3)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C4×C3⋊D3)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C4×(C3⋊D3)⋊C3)⋊C3 |
| Fitting | C4×C32⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C2×C4 |
537 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1703);