Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C22×C42 |
| direct product | C31×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C31 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ G | |
260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 4 generators on 47 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)(32,33,36,39)(34,41,42,38)(35,43,45,47)(37,40,46,44);(32,34,36,42)(33,38,39,41)(35,44,45,40)(37,43,46,47);(32,35)(33,34)(36,45)(37,38)(39,42)(40,43)(41,46)(44,47);(32,34)(33,35)(36,42)(37,43)(38,40)(39,45)(41,44)(46,47)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 242);