Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#10620184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊#10620184 |
| Fitting, socle | C34 ⋊ S4 |
| derived | C3×#1113⋊C3 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#1113⋊C3 | C2 |
| Fitting, socle | C34 | S4 |
| LCS | G ▷ C3×#1113⋊C3 | |
| UCS | C1 | |
234 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12 |
Polycyclic presentation:
2,3^2,2^2,3^3|b^a=b^2,c^a=c^2,d^a=e,e^a=d,f^a=g^2,g^a=f^2,h^a=h^2,d^b=e,e^b=de,f^b=g,g^b=h,h^b=f,g^d=g^2,h^d=h^2,f^e=f^2,h^e=h^227 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3879);