Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10619556⋊C3 |
| Sylow | #6910 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (#4176⋊C2)⋊C3 |
| commutator, cosocle | C2×#731 | C22×C3 |
| Frattini | C2×C32 | C3×D32 |
| Fitting | C2×#6910 | C22 |
| socle | C2×C3 | C3×((C3⋊D3)⋊C3)⋊C2 |
| hypocenter | #731 | C3×D4 |
| LCS | G ▷ C2×#731 ▷ #731 | |
| UCS | C1 ◁ C2 | |
248 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,e^3=h^2,b^a=bd,f^a=f^2,g^a=g^2h,e^b=e^2h,g^b=g^2,h^b=h^2,e^c=eh,f^e=fg,g^f=gh61 conjugacy classes — view the full character table.
| maximal subgroup of | #72229250, #72259590, #72259725, … |
| maximal normal subgroup of | #72259590, #72259725, #72259771 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1317);