Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C27⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C27⋊#622 |
| derived, Sylow | C32×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C27⋊#157 |
| commutator, hypocenter | C32×C27 | C8 |
| Frattini | C2×C9 | C3⋊#157 |
| Fitting | C2×C32×C27 | C4 |
| socle, prime radical | C2×C33 | Dic9 |
| cosocle | C27×C3⋊Dic3 | C2 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,f^3=g,g^3=h,d^a=de,e^a=de^2,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,d^b=d^2,e^b=e^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1129);