Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
| unambiguous semidirect product | Q8⋊H(5,𝔽3) |
| Fitting | C3×Q8×H(3,𝔽3) ⋊ C3 |
| Sylow | Q8 ⋊ H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C3 | C33×A4 |
| commutator, cosocle | C3×Q8 | C34 |
| Fitting | C3×Q8×H(3,𝔽3) | C3 |
| hypercenter | C2×C3×H(3,𝔽3) | A4 |
| hypocenter | Q8 | H(5,𝔽3) |
| LCS | G ▷ C3×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C3×H(3,𝔽3) | |
935 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^5,2^3|f^2=h,g^2=h,d^a=de,f^a=fg,g^a=f,c^b=ce,g^f=gh199 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3257);