Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6875 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C9 · Schur multiplier (H2) = C1 |
| direct product | C8×#6875 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C8 | C9⋊C9 |
| commutator | C9 | C3×C8×C9 |
| Frattini, cosocle | C3×C4×C9 | C2×C32 |
| socle | C2×C3 | C4×C9⋊C9 |
| prime radical | C2×C32 | C4×3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C8 ◁ C3×C8×C9 ◁ G | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8)(10,13,19,15,22,31,26,34,21)(11,16,27)(14,23,20,24,35,32,25,30,33)(17,29,28);(9,10,14,11,13,20,17,21,23,12,15,25,16,22,33,28,19,30,18,26,24,27,34,32,29,31,35)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 91);