Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | H(3,𝔽3)×C4⋊(C3⋊D3) |
| unambiguous semidirect product | C4⋊(C3⋊D3×H(3,𝔽3)) |
| Fitting | C32×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
1104 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3315);