Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (3−1+2⋊(C22⋊C9))⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (3−1+2⋊(C22⋊C9))⋊C2 |
| derived | 3−1+2⋊(C22⋊C9) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | 3−1+2⋊(C22⋊C9) | C2 |
| Frattini | C33 | C3⋊S4 |
| Fitting | C22×C3×3−1+2 | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ 3−1+2⋊(C22⋊C9) | |
| UCS | C1 | |
215 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 215 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^5,2^2|b^3=e,c^3=f^2,b^a=b^2e^2,c^a=c^2f,e^a=e^2,f^a=f^2,g^a=gh,c^b=cd,d^b=df,g^b=h,h^b=gh,d^c=df^251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 891);