Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×((C3⋊D3)⋊C3)⋊Dic3 |
| unambiguous semidirect product | ((C3⋊D3)⋊C3)⋊(C3×Dic3) |
| derived | C3×H(3,𝔽3) ⋊ C2×C3×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
745 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 745 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72228434, C3×Dic3×((C3⋊D3)⋊C3)⋊C2, C3×#13048339, … |
| maximal normal subgroup of | C3×Dic3×((C3⋊D3)⋊C3)⋊C2, C3×#13048339, #72259784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3063);