Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (((C3⋊D3)⋊C3)⋊C2)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×(((C3⋊D3)⋊C3)⋊C2)⋊D3 |
| unambiguous semidirect product | (((C3⋊D3)⋊C3)⋊C2)⋊(C3×D3) |
| Fitting, Sylow | C32×H(3,𝔽3) ⋊ D4 |
381 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72259765, D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3, #72259834, … |
| maximal normal subgroup of | D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3, #72259834 |
| maximal quotient of | #72259765, C3×#14519128 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3506);