Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#564 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C31 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C31 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ G | |
172 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 4 generators on 63 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(34,40)(35,43)(37,41)(38,45)(48,49,52,55)(50,53,58,56)(51,59,60,54)(57,62,63,61);(32,33,36,39)(34,41,40,37)(35,38,43,45)(42,47,46,44)(48,49)(50,56)(51,59)(52,55)(53,58)(54,60)(57,61)(62,63);(32,34,36,40)(33,37,39,41)(35,42,43,46)(38,44,45,47)(48,50)(49,53)(51,57)(52,58)(54,61)(55,56)(59,62)(60,63);(32,35)(33,38)(34,42)(36,43)(37,44)(39,45)(40,46)(41,47)(48,51,52,60)(49,54,55,59)(50,57,58,63)(53,61,56,62)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 245);