Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #6188⋊C32 |
| unambiguous semidirect product | (C3×#6188)⋊C3 |
| Sylow | H(5,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C3 | C32×#157 |
| commutator, hypocenter | H(3,𝔽3) | C32×C8 |
| Fitting, prime radical | C2×H(5,𝔽3) | C4 |
| cosocle | #1084 | C2×C32 |
| hypercenter | C2×H(3,𝔽3) | #157 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 ◁ C2×H(3,𝔽3) | |
250 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^2,2^2,3^3|a^2=d,d^2=e,f^a=fg,g^a=fg^2h^2,c^b=ch^2,f^d=f^2,g^d=g^2h,g^f=gh124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2982);