Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #6869⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6869⋊C8 |
| derived, Sylow | #6869 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #6869⋊C2 |
| commutator, hypocenter | #6869 | C8 |
| Frattini | C3×C4×C9 | C3⋊D3 |
| Fitting, cosocle | C4×#6869 | C2 |
| socle | C2×C3 | #66328 |
| prime radical | C2×C33 | Dic9 |
| LCS | G ▷ #6869 | |
| UCS | C1 ◁ C4 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,e^3=g,g^3=h^2,d^a=d^2,e^a=e^2g^2h,f^a=fh^2,g^a=g^2h,h^a=h^2,e^d=ef,f^e=fh120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 64);