Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#4184 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊#10619510 |
| derived, Sylow | C3×#731 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊#4184 |
| commutator, hypocenter | C3×#731 | C8 |
| Frattini | C32×C4 | C3⋊(C3⋊D3) |
| Fitting, cosocle | C3×C4×#731 | C2 |
| socle | C2×C32 | #1084 |
| prime radical | C2×C3×H(3,𝔽3) | Dic3 |
| LCS | G ▷ C3×#731 | |
| UCS | C1 ◁ C4 | |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,f^3=h^2,d^a=d^2,e^a=e^2,f^a=f^2h,h^a=h^2,f^e=fg,g^e=gh,g^f=gh^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 768);