Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×Dic3×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (Dic3×C3⋊D3)⋊C32 |
| unambiguous semidirect product | (C3×Dic3×C3⋊D3)⋊C3 |
| derived | C33 ⋊ C2×C32×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
729 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 729 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×PSU(3,𝔽2)⋊C3, C3×#67×(C3⋊D3)⋊C3, (C3⋊D3)⋊C3×#626, … |
| maximal normal subgroup of | C3×#67×(C3⋊D3)⋊C3, (C3⋊D3)⋊C3×#626, (C3⋊D3)⋊C3×#624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3011);