Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#6188) |
| derived, Sylow | C32×H(3,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C3⋊(C3⋊#157) |
| commutator, hypocenter | C32×H(3,𝔽3) | C8 |
| Fitting, prime radical | C2×C32×H(3,𝔽3) | C4 |
| socle | C2×C33 | #157 |
| cosocle | C32×#1084 | C2 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^a=de,e^a=de^2h^2,f^a=f^2,g^a=g^2,d^b=d^2,e^b=e^2h,e^d=eh108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2992);