Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9×3−1+2 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×AGL(1,ℤ/9) |
| commutator, cosocle | C2×C92 | C22×C3 |
| Frattini, socle | C2×C32 | C3×D32 |
| Fitting | C2×C9×3−1+2 | C22 |
| prime radical | C2×C33 | D32 |
| hypocenter | C92 | C3×Q8 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C2 | |
172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,e^3=h,f^3=g,b^a=bd,f^a=f^2g^2,g^a=g^2,e^b=e^2h^2,h^b=h^2,e^c=eh^2111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1188);