Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C9⋊#6296 |
| Sylow | C33×C9 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊#1113 |
| commutator, Fitting, cosocle | C2×C33×C9 | C22 |
| Frattini | C2×C3 | C3⋊#1113 |
| socle, prime radical | C2×C34 | C2×D3 |
| hypocenter | C33×C9 | Q8 |
| LCS | G ▷ C2×C33×C9 ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
558 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,e^3=h,b^a=bc,d^a=d^2,e^a=e^2h^2,g^a=g^2,h^a=h^2,d^b=d^2,e^b=e^2h^2,f^b=f^2,h^b=h^2171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3211);