Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10619897⋊C3 |
| Sylow | C32×3−1+2 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66431⋊C3 |
| commutator, cosocle | C2×C32×C9 | C22×C3 |
| Frattini | C2×C3 | C3×#1113 |
| Fitting | C2×C32×3−1+2 | C22 |
| socle | C2×C33 | C2×C3×D3 |
| hypocenter | C32×C9 | C3×D4 |
| LCS | G ▷ C2×C32×C9 ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
492 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 55 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:
2^2,3,2,3^4|e^3=h,b^a=bd,e^a=e^2h^2,g^a=g^2,h^a=h^2,e^b=e^2h^2,f^b=f^2,h^b=h^2,e^c=eh^293 conjugacy classes — view the full character table.
| maximal subgroup of | #72229035, #72259536, D3×#6192⋊C3, … |
| maximal normal subgroup of | #72259536, D3×#6192⋊C3, #72259642 |
| maximal quotient of | #72229035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3135);