Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | Q8⋊#6855 |
| Sylow | Q8 ⋊ #6855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical | C2×C33 | C3×A4 |
| commutator | C3×Q8 | C92 |
| Fitting | C32×Q8×C9 | C3 |
| cosocle | C33×Q8 | C32 |
| hypercenter | C2×C32×C9 | A4 |
| hypocenter | Q8 | #6855 |
| LCS | G ▷ C3×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C33 ◁ C2×C32×C9 | |
257 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1944 |
Polycyclic presentation:
3^5,2^3|a^3=e,b^3=c,f^2=h,g^2=h,b^a=bd,f^a=fg,g^a=f,g^f=gh279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 277);