Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C4×#6880 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | #732 |
| commutator | C3×C9 | C2×C32×C4 |
| Frattini, cosocle | C2×C3×C9 | C22×C32 |
| socle | C22×C3 | C2×#732 |
| prime radical | C22×C32 | C2×H(3,𝔽3) |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C2×C32×C4 ◁ C2×C3×C4×C9 ◁ G | |
168 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2)(7,8,11,10,14,21,17,26,20)(9,13,18,16,23,19,28,33,30)(12,22,32,24,31,15,25,29,27);(3,4,5,6)(8,12,23,14,24,33,26,25,13)(11,18,29,20,30,31,21,19,22)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 611);