Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10620070 |
| commutator, Fitting, cosocle, hypocenter | C22×C32⋊C9 | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C22×#4181 | C3 |
| LCS | G ▷ C22×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
204 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 27 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:
2,3,2^2,3^4|b^3=g,f^3=h^2,e^a=e^2,f^a=f^2h,h^a=h^2,c^b=d,d^b=cd,e^b=eh,f^e=fg60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2622);