Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #92299⋊C4 |
| derived | C92 ⋊ C2×C3×C4 |
| Sylow | C9×3−1+2 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×AGL(1,ℤ/9) |
| commutator, hypocenter | C92 | C2×C3×C4 |
| Frattini, socle | C2×C32 | C3×D32 |
| Fitting | C2×C9×3−1+2 | C22 |
| prime radical | C2×#92299 | C2 |
| cosocle | C2×C92 | C22×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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:
2^2,3,2,3^4|a^2=d,b^2=d,e^3=h,f^3=g,f^a=f^2g^2,g^a=g^2,e^b=e^2h^2,h^b=h^2,e^c=eh^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72228948, #72228952, C2×#92299⋊C4 |
| maximal normal subgroup of | #72228948, #72228952, C2×#92299⋊C4 |
| maximal quotient of | C2×#92299⋊C4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1184);