Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C3⋊D9)⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | (C3⋊D9)⋊#157 |
| Fitting, derived, Sylow | C33×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C33×C9 | C2×C4 |
| Frattini | C3 | #10620197 |
| socle | C34 | C4×D3 |
| prime radical | C3⋊D3×C3⋊D9 | C2 |
| cosocle | C3×C9×C3⋊D3 | C22 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
384 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^5|b^2=c,g^3=h^2,f^a=f^2,g^a=g^2h,h^a=h^2,d^b=de^2,e^b=d^2e^2,f^b=f^2,d^c=d^2,e^c=e^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3494);