Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | C4⋊((C3⋊D3)⋊H(3,𝔽3)) |
| unambiguous semidirect product | (C4⋊(C3⋊D3))⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C4⋊((C3⋊D3)⋊C3))⋊C3 |
| Fitting | C4×C32⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C32⋊H(3,𝔽3) ⋊ D4 |
537 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3^2,2,3^3|b^2=e,b^a=be,g^a=g^2,h^a=h^2,d^c=df,g^d=gh135 conjugacy classes — view the full character table.
| maximal subgroup of | #72229211, #72259895, D4×(C3⋊D3)⋊H(3,𝔽3), … |
| maximal normal subgroup of | #72259895, D4×(C3⋊D3)⋊H(3,𝔽3), #72259923 |
| maximal quotient of | #72229211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1704);