Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C3⋊#10619761 |
| derived | C3×C32⋊(C22⋊C9) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C3⋊((C22⋊C9)⋊C2)) |
| commutator, cosocle, hypocenter | C3×C32⋊(C22⋊C9) | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C3×C32⋊(C22⋊C9) | |
| UCS | C1 ◁ C3 | |
660 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 91 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:
2,3^5,2^2|b^3=f,b^a=b^2f^2,c^a=c^2,d^a=d^2,f^a=f^2,g^a=gh,d^b=de,g^b=h,h^b=gh99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2518);