Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | H(3,𝔽3)×#624 |
| unambiguous semidirect product | (C32×#624)⋊C3 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
735 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 735 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | (C3⋊D3)⋊C3×#624 |
| maximal normal subgroup of | (C3⋊D3)⋊C3×#624 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3022);